James Wade, Dave Chisnall and Daryl Gurney all also enjoyed victories as Friday's quarter-final line-up was completed with the remaining six games from round three in the £1.65 million tournament.
Top seed Van Gerwen hit a brilliant 170 finish and averaged over 104 in a 4-1 victory against the tenacious Darren Webster, who threatened to take the game into a sixth set with a late rally.
The world number one and odds-on favourite to win the title with sponsors William Hill has averaged over 100 in all three of his matches so far and will now take on Gurney in the quarter-finals.
"I feel good," said 2014 World Champion Van Gerwen, who hit eight 180s in his defeat of Webster.
"I struggled at times and Darren played really well but I know I can play under pressure and I showed I can do anything at the right time.
"I'm the winning man and that is what matters. The only thing that counts for me is winning this tournament and I'm now one step closer."
Taylor, meanwhile, also averaged over 100 in a 4-2 success over Kim Huybrechts to set up a tasty last eight encounter with his long-standing rival Van Barneveld.
The number four seed missed darts to seal a whitewash win but eventually saw off his Belgian opponent in six sets to keep his bid for an incredible 17th World Championship title on course.
"I put Kim under tremendous pressure and it paid off," said Taylor, who shared 14 180s with his opponent during the contest.
"My game against Raymond will be the game of the tournament. It's going to be buzzing in Alexandra Palace.
"I'm going to relax and enjoy it and, if I get through it, I think I can win another World Championship title."
2014 finalist Wright continued his impressive progress as he also averaged in excess of 100 for the third consecutive match, having only dropped three legs in two previous straight sets victories.
Number three seed Wright won nine out of the first ten legs to open up a three set lead before eventually seeing off Ian White 4-1, defying six 180s from his opponent.
"I feel happy," said Wright, who will take on Wade in Friday's quarter-finals.
"Ian started to show what he could do towards the end of the match but I've got a strong mind-set and that saw me through.
"I've been playing well and averaging over 100 but that is the standard you need to hit in every match for it to be possible to become World Champion."
Wade had earlier produced an amazing comeback to defeat Michael Smith, winning seven straight legs to overturn a 3-1 deficit in sets as he kept on course his bid to be crowned as World Champion for the first time.
The three-time semi-finalist produced two 121 finishes in the fightback, and admitted: "I'm so happy that I won.
"It was a strange game, where neither of us reflected our true abilities but the crowd were brilliant and gave me an extra 20 percent."
Number seven seed Chisnall fended off the threat of 2016 semi-finalist Jelle Klaasen, hitting a dozen 180s as he reached the last eight at Alexandra Palace for the first time in his career.
Chisnall, who has reached three televised finals in 2016, moved a step closer to another after coming back from two legs down in the sixth set to deny Klaasen a decider.
"I'm scrapping hard and I'm glad to win," said Chisnall, who faces reigning champion Gary Anderson in Friday's quarter-finals.
"I played okay and that was good enough so I'm over the moon. I want to play better and I know I can. I'll have to step it up against Gary but I know I can do it."
Gurney became the first Northern Irish player to reach the quarter-finals of the World Championship by coming through a nail-biting encounter with two-time semi-finalist Mark Webster.
The number 24 seed, who also reached the quarter-finals of the World Grand Prix in October, squandered six match darts - including five for a 4-2 triumph - before finally prevailing in a deciding set.
"I'm just really relieved," admitted Gurney, who is the last man to defeat Van Gerwen, 25 matches ago in a European Tour event in October.
"I should've won it earlier but my doubles for the match were dreadful. In the end I won, I'm through and that's the most important thing."
Friday sees the quarter-finals played out over two sessions, with Wright and Wade kicking off the afternoon's action before defending William Hill World Champion Anderson takes on Chisnall.
Van Gerwen returns to the Alexandra Palace stage in the evening to face off with Gurney and the showdown between Taylor and van Barneveld will see the field reduced to the final four.
William Hill World Darts Championship
Thursday December 29
Mark Webster (25) 3-4 Daryl Gurney (24)
Dave Chisnall (7) 4-2 Jelle Klaasen (10)
James Wade (6) 4-3 Michael Smith (11)
Peter Wright (3) 4-1 Ian White (14)
Phil Taylor (4) 4-2 Kim Huybrechts (13)
Michael van Gerwen (1) 4-1 Darren Webster
Friday December 30
Afternoon Session (1pm)
James Wade (6) v Peter Wright (3)
Gary Anderson (2) v Dave Chisnall (7)
Evening Session (7pm)
Michael van Gerwen (1) v Daryl Gurney (24)
Raymond van Barneveld (12) v Phil Taylor (4)
Quarter-Finals - Best of nine sets