Legendary star Taylor has won 15 World Matchplay titles since the tournament was introduced in 1994, including seven in a row from 2008-2014, but was made to work hard before securing a 10-8 win.
Green - who secured the final qualifying place in Blackpool at the last Players Championship before the cut-off earlier this month - opened his first World Matchplay appearance in 12 years with a pair of 14-dart legs to lead Taylor 2-0.
The Stoke legend hit back to level before Green landed two 180s in leg five to move 3-2 up only to see the 55-year-old win three in a row to turn the game around.
Missed doubles in successive legs from Taylor, though, allowed Green back in to level at five-all, but finishes of 118 and 70 from the number three seed steadied his nerves before he closed out the win.
"It was tough tonight and Robbie played well but sometimes a good battle like that sets you up for a tournament because you go into the next round ready and feel more prepared for the stage," said Taylor, who now faces Mensur Suljovic in Wednesday's second round.
"Robbie came out to win and fair play to him - he believed in himself and hit the finishes, and he put me under pressure. I'd just seen Barney get beaten before I went on stage and then I was 2-0 down and I thought I was going out too, but I got through.
"The more I'm in it the better I'll get. I love this event and this stage and I get a lot of support, so I'm giving it my best. There's something about this event."
Merseyside's Green said: "I'm quite proud of myself because there's no shame losing to Phil, he's the best-ever and he's still my idol. I love him to bits - I remember standing out in the crowd watching him as a fan, singing his name like everyone else.
"In some legs I really had to dig deep and keep going, he missed and let me in a couple of times and at times I let him off the hook, but I'm made up to have given a good account of myself."
Northern Ireland's Dolan put a difficult year behind him as he overcame 2010 World Matchplay finalist van Barneveld 10-7 with a fine display to move through to a second round meeting with Mervyn King on Wednesday.
A tight opening saw the first eight legs shared before Dolan, who had earlier taken out 104, took the game's first break of throw in a run of three successive legs to open up a 7-4 lead before adding a 105 checkout as he held on for the win.
Dolan has slipped out of the world's top 20 in the past year, but admitted: "This is an absolutely brilliant result for me and a massive win.
"Raymond is one of the greatest players to ever lift a dart so it's a great achievement for me. It means a lot because I've not had a great 12 months but I can see glimpses of what I've been doing in practice up there on stage and it gives me a lot of confidence.
"My finishing held up and I think that's what won me the game. My double 16 was crucial at times, and it's fine margins in a game like that so I'm glad to come out on the right side of it."
Steve Beaton won through to the second round for the first time since 2012 with a 10-6 defeat of Jelle Klaasen, as the number ten seed fell to defeat despite a spirited fightback.
Beaton produced some fine darts to open up an early 4-1 lead, hitting two 180s and a 13-dart finish in the process, only to see his Dutch rival respond to cut the gap to 5-4.
Klaasen, though, crucially missed two darts to level the game in leg ten before seeing Beaton edge into an 8-4 lead, and though Klaasen finished 81 and 82 to halve the deficit he was unable to prevent his opponent closing out victory with an 11-darter.
"At 4-1 I was going okay but Jelle came back at me like a train, like you know he can," said Beaton. "To be 6-4 up at the second break meant I had a bit of a cushion and when I got out to 8-4 it was mine to lose after that.
"I've been practising well and I've picked up my game recently, but I've probably never fulfilled myself on TV. Even at 52 I'm still as competitive as the rest and it's a great buzz, the crowd are brilliant and that's what you play for."
Beaton now meets former World Youth Champion Michael Smith, who overcame Simon Whitlock 10-6 with a strong second half of their contest.
Whitlock led three times as he shared the opening six legs, and took out 105 to level at four-all before Smith produced a key run of four successive legs to move 8-4 up.
Whitlock took two of the next three, but an 11-darter from Smith had moved him to the brink of victory before he sealed his second round spot on double five.
"I wasn't firing on all cylinders but I'll take the win and I'm through to the next round," said Smith. "I started off really slow but started to get in to it later on.
I've never been too good at the World Matchplay, I think this is only the second time in five years that I've made the second round so it's about that that I turned up. I'm number seven in the world so the minimum should be the last eight but I'll take it one step at a time."
The second round of the £450,000 tournament begins on Tuesday, with reigning champion Michael van Gerwen back in action as he takes on Australia's Kyle Anderson.
Former finalist Adrian Lewis meets Gerwyn Price at the last 16 stage for the second successive year, with the Welshman winning 12 months ago, while World Grand Prix champion Robert Thornton plays Dave Chisnall and number five seed Peter Wright takes on Ian White.
BetVictor World Matchplay
Monday July 18
Jelle Klaasen 6-10 Steve Beaton
Raymond van Barneveld 7-10 Brendan Dolan
Phil Taylor 10-8 Robbie Green
Michael Smith 10-6 Simon Whitlock
Tuesday July 19 (7pm)
Second Round x4
Robert Thornton v Dave Chisnall
Peter Wright v Ian White
Michael van Gerwen v Kyle Anderson
Adrian Lewis v Gerwyn Price
Wednesday July 20 (7pm)
Second Round x4
Mervyn King v Brendan Dolan
Michael Smith v Steve Beaton
Phil Taylor v Mensur Suljovic
Gary Anderson v Terry Jenkins
Jelle Klaasen v Steve Beaton
0-1 - Beaton fires in a 180 before finishing 80 on tops to break throw in the opening leg.
0-2 - Double 18 sees the former World Matchplay semi-finalist double his lead.
1-2 - Klaasen takes out 58 on tops to claim his first leg.
1-3 - Both players initially miss one dart at a double before Beaton returns on double eight to regain his cushion.
1-4 - Beaton lands his second 180 before punishing Klaasen's miss at double 11 by landing double two.
2-4 - Klaasen lands two 180s in a superb 11-darter as double 18 sees him respond with a break of throw.
3-4 - Klaasen finishes 76 in two darts to reduce the gap to one leg.
3-5 - Two misses from Klaasen at double 18 allow Beaton back in on double 16.
4-5 - Klaasen completes a 14-dart leg on tops to reduce the gap further.
4-6 - Klaasen misses two darts to level, at double 14 and seven, and Beaton pins tops to edge two legs clear.
4-7 - Beaton breaks throw for a third time, taking out 50 on double 16 to move three legs up once again.
4-8 - Beaton wires the bull to finish 164, but three misses at double 14 from the Dutchman allow him back to land double eight.
5-8 - Klaasen wins his first leg in four, taking out 81 on double 18.
6-8 - Beaton lands a 180, his third, but misses two darts at double 16 to allow Klaasen in for a break of throw as he finishes 82 on double eight.
6-9 - Beaton finishes 61 on double nine to move a leg away from victory.
6-10 - Beaton completes the win in style with an 11-darter, hitting a 177 before landing double 16 to move into the second round.
Raymond van Barneveld v Brendan Dolan
0-1 - van Barneveld lands a 180 but misses two darts at doubles to break throw before Dolan hits tops to lead.
1-1 - The Dutchman levels with a 61 finish on double 18, despite a maximum from Dolan.
1-2 - van Barneveld misses double 12 for a 141 finish, and Dolan lands double ten to edge back in front.
2-2 - van Barneveld hits back to level.
2-3 - Dolan finishes 104 as he moves back ahead.
3-3 - Both players land 180s before van Barneveld finishes double 18 for a 13-darter.
3-4 - Dolan lands his fourth maximum of the game before finishing 61 on double 18 to move back ahead with a 14-dart finish.
4-4 - Double eight sees the 2010 finalist level.
4-5 - van Barneveld misses double 18 to break throw, and Dolan finishes 62 on double 16 to edge in front once more.
4-6 - Dolan breaks for the first time in the game to open up a two-leg lead.
4-7 - Dolan consolidates his lead by winning a third successive leg.
5-7 - van Barneveld hits back on double ten.
5-8 - van Barneveld misses the bull for a 121 finish to break throw, and Dolan takes out 105 on double 16 to move two legs away from the win.
6-8 - Dolan is unable to land tops to punish van Barneveld for three misses, as the Dutchman returns on double two to cut the gap.
6-9 - Dolan lands a third-dart double six to move to the brink of victory.
7-9 - Tops sees van Barneveld keep his hopes alive.
7-10 - Dolan is first to a finish before landing double 16 to complete a brilliant performance as he moves into the last 16.
Phil Taylor v Robbie Green
0-1 - Green wins the opening leg with a 14-dart finish.
0-2 - The qualifier doubles his lead, opening with a 177 before Taylor lands a 180, but Green then adds a maximum of his own before punishing a miss from the 15-time champion to finish double four for another 14-darter.
1-2 - Green misses double ten for a 128 checkout to win a third leg, and Taylor breaks throw to get off the mark.
2-2 - Taylor opens with a 180 before finishing double eight for a 64 checkout to level.
2-3 - Both players open the leg with maximums before Green adds a second maximum and finishes 25 to regain the lead.
3-3 - Taylor levels on double 16.
4-3 - The 15-time champion takes another break of throw to lead for the first time by finishing 64.
5-3 - Taylor finishes 57 on tops to move two legs clear.
5-4 - Taylor lands a 180, but misses five darts at doubles as Green recovers to land tops and win his first leg in four.
5-5 - Taylor's double trouble continues as he misses five darts at double 16 and eight, allowing Green an escape from his own misses in two visits to land double one and level.
6-5 - Taylor takes out 118 on double 19 to regain his range and break throw to move back in front.
7-5 - Taylor hits a 180 before taking out 70 on tops to move two legs clear.
7-6 - Green fires in a maximum and finishes double ten to respond.
8-6 - Both players land 180s, but Green crucially misses a dart at tops to level as Taylor returns on double nine to regain breathing space.
8-7 - Green hits a sixth 180 and tops as he pulls back a leg.
9-7 - Double 16 sees Taylor move one leg away from a hard-fought victory.
9-8 - Taylor lands a maximum to leave a two-dart finish, but Green holds his nerve to finish double 16 for a 14-darter to keep the game alive.
10-8 - Green lands his seventh 180, but Taylor finishes 65 on tops for a tough win.
Michael Smith v Simon Whitlock
0-1 - Whitlock opens with a 180 and Smith also lands a maximum before the Australian lands double 12 to win the opener.
1-1 - Whitlock adds another 180 but misses ten darts at doubles before Smith, with his seventh dart at a double, levels on double one.
1-2 - Whitlock finishes 68 on double 16 to regain the lead.
2-2 - Whitlock wires the bull to finish 170, and Smith steps in on double top to avert a possible break of throw.
2-3 - The Australian edges back ahead by winning leg five.
3-3 - Smith takes out 87 to level again.
4-3 - Smith breaks throw on double four, after being given a reprieve for missed doubles when Whitlock is unable to land tops for a 120 finish.
4-4 - Whitlock hits back by landing a 105 checkout.
5-4 - Smith moves back ahead with a second break, hitting a 180 and double ten.
6-4 - The former World Youth Champion claims a second successive leg to move two clear for the first time.
7-4 - Smith finishes 100 to win a third successive leg.
8-4 - Smith moves four legs clear by taking out 40.
8-5 - The pair trade 180s before Whitlock finishes 62 on double 16 to win his first leg in five.
9-5 - Both players land maximums again, with Smith finishing 88 on double 14 for an 11-darter to move a leg away from the win.
9-6 - Smith fires in his fifth 180, but it comes too late as Whitlock finishes double 18 to keep his hopes alive.
10-6 - Whitlock misses three darts at doubles to continue his challenge, and Smith returns on double five to claim his second round place.