Brunson set a franchise playoff scoring record and also became the first player in franchise history to post at least 30 points and 10 assists in consecutive playoff games.
The Knicks lead the series 3-1 with Game 5 set for Tuesday in Philadelphia.
Brunson appeared his injure his knee at the end of the third quarter but returned a few minutes into the fourth. He shot 18 of 34 from the field and 9 of 11 from the free-throw line.
Brunson knocked down two free throws with 5.2 seconds remaining for a five-point lead, 97-92.
OG Anunoby added 16 points and 14 rebounds, Miles McBride scored 13 and Josh Hart pulled down 17 rebounds.
New York centre Mitchell Robinson missed the second half of Game 3 with a sprained left ankle and was ruled out for Game 4.
Joel Embiid led the Sixers with 27 points, 10 rebounds and two blocked shots. Tyrese Maxey scored 23 points, Kelly Oubre Jr. added 19 and Tobias Harris had 10.
The Sixers trailed 95-92 after Kyle Lowry hit 1-of-2 free throws with 7.5 seconds left.
The Knicks took an 86-81 lead when Anunoby scored with 8:09 left in the fourth quarter.
Maxey hit a twisting layup with 7:35 remaining to close the Sixers within three, 86-83.
The Sixers jumped out to a 27-17 lead at the end of the first quarter.
Philadelphia went cold and missed 12 straight shots during one stretch in the second quarter. When Brunson hit a tough turnaround jumper with 5:31 left, the Knicks went ahead 34-32.
New York forward Bojan Bogdanovic sustained a left foot contusion just 19 seconds into the second and went to the locker room. Bogdanovic, who was ruled out shortly after halftime, was already reportedly playing with ligament damage in his left wrist.
Oubre hit a 3-pointer from the wing with 3:15 remaining and the Sixers led 42-37.
The Sixers led 49-47 at halftime thanks in large part to 27 points combined from Embiid (14) and Maxey (13).
Brunson led all players with 23 at halftime.
The Sixers took a 61-51 advantage in the third quarter, but Brunson responded with a three-point play with 6:50 left in the third to cut the deficit to seven.
Embiid soon committed consecutive turnovers and Brunson hit a tough bank shot with 4:48 to go to close within 63-60.
The Knicks led 77-76 at the end of the third.
