Van Barneveld went into his decisive third Group E clash with American Larry Butler knowing that the winner would join Anderson in moving through to the last 16.
Former World Matchplay winner Butler provided typically stiff opposition as he hit back from 2-0 down to level, but the American ace crucially missed darts at doubles to lead 3-2 and 4-3.
Van Barneveld capitalised as an 84 checkout put him 4-3 up before a 70 finish completed a 5-3 win and moved the 2012 Grand Slam of Darts champion through to the knockout stages.
"At two-all there was a lot of pressure on my shoulders because I wanted to win so badly and I'm really pleased with the win," said van Barneveld.
"I've known Larry for a lot of years and I knew how good he is but he missed a few doubles and let me in, and my finishing helped me - and these doubles were so important."
Anderson completed a clean sweep in Group E with his 5-1 win over Andy Boulton, averaging over 100 for a third successive game as he condemned the Ayrshire-based qualifier to a trio of defeats.
"I'm happy with the way my darts are going," said Anderson. "It's been alright so far and even though I didn't hit as many 180s as I wanted to tonight I hit my doubles well.
"I'd love to go on and win this tournament now. It's my favourite event but the players are getting harder and harder so I've got to take it one match at a time.
"In the group stage it's first to five and anything can happen, but I prefer the longer games and I can settle into that now on Wednesday in the second round."
Reigning champion Phil Taylor also moved through to the knockout phase with three straight wins as he defeated Austrian youngster Rowby-John Rodriguez 5-2.
"It was a hard game so I'm pleased to win and to have three wins is the dream coming into the groups," said Taylor
"Rowby went out there to enjoy himself and gave it his best shot, and he was hitting 180s for fun but he missed a couple of doubles. He's a good little player who's full of confidence and full of ability."
Taylor added: "It will be a scrap against Terry but it's a longer format. It's been a tough three days but I can get ready for that now."
Robbie Green joined Taylor in qualifying from Group H after defeating Martin Phillips 5-1 in their decider, with the Wallasey-based qualifier finishing five doubles from six attempts to reach the second round for a second successive year.
"I was a bit nervous about tonight and I had to see this as a straight knockout game," admitted Green. "Martin's a very good friend of mine so it was difficult emotionally and a really tough game, but I'm just happy to go through.
"I won through a tough qualifiers and now it's time to show what I can do on the stage. I don't think I've shown anywhere near my potential yet, so hopefully that's still to come."
October's World Grand Prix champion Robert Thornton hit back from 4-2 down to edge a 5-4 win over Terry Jenkins which saw him top Group G with three wins from as many matches.
Jenkins moved into a 4-2 lead with a 136 checkout as he secured his own progression, but was unable to claim a win which would have seen him top his group as five missed match darts were punished by Thornton as he took the final three legs.
"Terry was due a cracking game and he produced it tonight, and I had to fight all the way to get the win and it's great to finish top," said Thornton.
"I've won my group before and I'm happy to have won all three games. My scoring's holding up well and I'm playing okay."
Jenkins' narrow defeat meant that he qualified ahead of Geert De Vos and Jonny Clayton on leg difference, despite the Belgian's brilliant 5-0 whitewash in his final group game.
Clayton had defeated Jenkins in their opener on Saturday, but the Welshman was denied a dart at a double by a superb performance from De Vos, who hit the Grand Slam of Darts' second highest ever average in a win which ultimately came in vain.
"I'm very pleased and that's definitely my best performance," said De Vos. "I know I can play well and that came through tonight - my first game was good as well but I missed a few doubles."
James Wade, the 2010 Grand Slam of Darts finalist, won Group F with a third straight victory as he defeated Keegan Brown 5-2, coming from a leg down to average over 100 for a second successive game.
"I didn't know the scenarios and I felt a nervous going up there, and I played the best I could in the situation I was in," said Wade, who now faces van Barneveld in the second round.
"It was a funny game because Keegan had chances, but I'm hitting doubles and hitting scores and I can only take positives from that. I've never practised as much as I am now and hopefully it's the time that it's going to come out.
"It's another good performance so I'm happy."
Brown's defeat meant that Mark Webster qualified alongside Wade following a nervous wait, with the Welsh left-hander having earlier defeated Dutchman Michel van der Horst 5-3 from 2-0 down in their final group game.
"I'm feeling pleased," said Webster. "I held up my half of the bargain and I think I deserved to go through - I've had a pretty steady group and won two of my three games.
"Keegan's a talented player and I knew he could beat James, but James put in a professional performance and I knew he'd want to win. It's a big ask to beat James because he's one of the favourites for the competition."
Webster now meets Anderson in Wednesday's second round, and he said: "He's the World Champion but I'm improving every day and I've got to test myself at a level so let's see where I'm at.
"He's an unbelievable player, a big 180 scorer but it's a good place to see where I'm at. I'm not defeatist - I think I can win - but I've got to take my chances. It will be a good game and I've got to try and put him under pressure when I can."
The round-robin phase of the £400,000 tournament concludes on Tuesday as Groups A-D play their final matches, with only nine-dart hero Dave Chisnall certain of his second round place going into the third games.
Michael van Gerwen, Martin Adams and Michael Smith have one foot into the last 16 following two victories so far, while Mervyn King and Peter Wright face a shoot-out in Group D to determine who qualifies alongside Chisnall.
SINGHA Beer Grand Slam of Darts
Monday November 9
Groups E-H Final Games
Jonny Clayton 0-5 Geert De Vos (G)
Robbie Green 5-1 Martin Phillips (H)
Mark Webster 5-3 Michel van der Horst (F)
Gary Anderson 5-1 Andy Boulton (E)
Robert Thornton 5-4 Terry Jenkins (G)
Phil Taylor 5-2 Rowby-John Rodriguez (H)
James Wade 5-2 Keegan Brown (F)
Raymond van Barneveld 5-3 Larry Butler (E)
Second Round Fixtures
Gary Anderson v Mark Webster
James Wade v Raymond van Barneveld
Robert Thornton v Robbie Green
Phil Taylor v Terry Jenkins
Wednesday's order of play TBC
Tuesday November 10 (7pm-11pm)
Groups A-D Final Games
Dave Chisnall v Scott Mitchell (D)
Ian White v Jelle Klaasen (B)
Kim Huybrechts v Mark Oosterhuis (A)
Adrian Lewis v Wayne Jones (C)
Michael van Gerwen v Steve West (A)
Peter Wright v Mervyn King (D)
Steve Beaton v Martin Adams (B)
Michael Smith v Andy Fordham (C)
Best of nine legs
Jonny Clayton v Geert De Vos
0-1 - De Vos' 177 is countered by a 180 from Clayton, but double six for a 14-darter moves the Belgian ahead.
0-2 - Clayton lands another 180, but De Vos takes out tops for a 13-darter to double his lead.
0-3 - De Vos lands two maximums in a 12-darter as he finishes 79 on tops to win a third leg.
0-4 - De Vos scores 171 before finishing 90 on double ten for a 12-darter.
0-5 - De Vos takes out 85 on double 12 as he seals victory with a stunning 113.86 average - the second highest ever in the event's history.
Robbie Green v Martin Phillips
1-0 - Tops gives Green the opening leg.
2-0 - Phillips' missed doubles prove costly as Green takes out double 16.
3-0 - Green wins his third successive leg as he pulls clear by finishing 60 on tops.
3-1 - Phillips takes out 76 on tops as he wins his first leg of the game.
4-1 - Green fires in a 180 and takes out 43 for a 14-darter.
5-1 - Green seals victory in style with an 11-dart leg, hitting two 180s and double 16.
Mark Webster v Michel van der Horst
0-1 - A miss from Webster allows van der Horst in to finish 81 on double 12 for the opener.
0-2 - Tops sees the Dutch qualifier move two legs up.
1-2 - Webster hits a 180, and is given a let-off for three missed doubles as van der Horst misses double 16, allowing the left-hander back in on double two.
2-2 - Webster levels the game on tops.
2-3 - Webster misses the bull for a 170 checkout, allowing van der Horst in to finish double 16 for a 14-darter.
3-3 - Double 12 for Webster sees him level again.
4-3 - van der Horst misses double top and ten, allowing Webster in to finish 60 on double ten to break throw and move ahead.
5-3 - Webster takes out a third-dart double six to secure the win.
Gary Anderson v Andy Boulton
1-0 - Double 12 gives the World Champion the opening leg.
1-1 - Boulton levels by taking out 101.
2-1 - Double eight edges Anderson back ahead.
3-1 - The Scot finishes 121 for a key 12-darter.
4-1 - Anderson lands double eight again as he moves three legs clear.
5-1 - Anderson hits a 180 before finishing double 12 for a 14-darter to complete the group stage with three wins.
Robert Thornton v Terry Jenkins
0-1 - Double ten gives Jenkins the opening leg.
1-1 - Thornton levels by finishing tops for a 14-darter.
1-2 - A superb 11-dart finish sees Jenkins regain the lead.
2-2 - Thornton responds once more by finishing double ten.
2-3 - Jenkins fires in a 180 as double two edges him ahead.
2-4 - Thornton lands a 180, but Jenkins breaks throw with a brilliant 136 checkout.
3-4 - Thornton fires in another maximum, and when Jenkins misses double 12 for a 104 finish, the Scot takes out tops for a 14-darter to break throw immediately in reply.
4-4 - Thornton hits a 180 for a third successive leg before finishing 105 for a 12-darter to force a deciding leg.
5-4 - Jenkins sees a further four match darts slip away to allow Thornton a reprieve for an earlier miss at tops as he returns to hit the bed and claim the win - taking top spot in Group G as Jenkins finishes second.
Phil Taylor v Rowby-John Rodriguez
1-0 - Rodriguez kicks off the game with a 180, but Taylor takes the leg on double eight.
1-1 - Taylor lands a 180, but two missed doubles allow the Austrian youngster to level on tops.
2-1 - Rodriguez opens with a 180 and adds a 177 only to then burst his score when aiming for double eight, allowing Taylor to capitalise.
3-1 - Rodriguez lands another maximum, but further missed doubles give Taylor his chance to open up a two-leg lead.
4-1 - Rodriguez hits his fourth maximum, but Taylor takes out 41 to move three legs clear.
4-2 - The youngster finishes 60 on tops to reply.
5-2 - Double 16 sees Taylor seal the win and top Group H, with Rodriguez's defeat meaning that Robbie Green finishes in second place.
James Wade v Keegan Brown
0-1 - Two misses from Wade allow Brown in to take out 90 on the bull to claim first blood.
1-1 - Wade hits a 180 and double ten to level.
2-1 - Two missed doubles from Brown allow Wade in on double 12.
2-2 - Brown hits a 180, and when Wade misses the bull to take out 121, the Isle of Wight youngster finishes 100 in style with two double tops.
3-2 - Wade fires in a 177 score to leave 24, and when Brown misses three further doubles, the left-hander takes out double six to regain the lead.
4-2 - Wade finishes 85 on the bull to move to the brink of victory.
5-2 - Brown misses double 16 for a 134 checkout, and Wade takes out 80 to claim the win, completing a clean sweep in the group stage.
Raymond van Barneveld v Larry Butler
1-0 - Both players land 180s in the opening leg, which van Barneveld wins on double 16 for a 14-darter.
2-0 - Double 12 sees van Barneveld continue his confident start.
2-1 - Butler finishes 72 on tops to hit back.
2-2 - van Barneveld fires in a 180 to leave 41, but Butler finishes 100 for a 12-darter to level.
3-2 - Butler hits a 180 of his own, but misses two darts at double eight to allow van Barneveld back in on tops.
3-3 - Butler lands a third 180 of the game, and double six punishes van Barneveld's miss at double top as the American levels.
4-3 - Butler misses tops to move 4-3 up, and van Barneveld takes out 84 on double 12 in a key leg.
5-3 - Butler hits a 174 score as he bids to force a decider, but a miss at double 18 allows van Barneveld to take out 70 on double for to claim victory and a place in the second round.