Antetokounmpo recorded his 13th 30-point game of the season and added 14 rebounds for his 22nd double-double, but it was his performance in the third that helped the Bucks get a win in their first appearance on Christmas since facing the Kansas City Kings in 1977.
His 30 points also made him the first Milwaukee player to score 30 on Christmas Day since Kareem Abdul-Jabbar in 1972.
Milwaukee won for the fifth time in six games overall.
Coming off a season-low nine points Saturday in Miami, Antetokoumpo made 5 of 6 shots in the third when the Bucks shot 65% (15 of 23) and outscored New York 36-22.
He hit two layups, converted a dunk and hit two jumpers during the decisive quarter and helped the Bucks avenge a 136-134 overtime loss in New York on Dec 1 when they blew a 16-point lead.
Brook Lopez added 20 points as the Bucks shot 54.7 percent and outscored the Knicks 61-49 in a flawless second half. Malcolm Brogdon contributed 17 while Thon Maker chipped in 12 to help Milwaukee compensate for a rough showing by Khris Middleton, who was 2 of 12.
Rookie Kevin Knox scored 21 points for the Knicks, who dropped their sixth straight Christmas Day game since beating Boston in 2011.
Knox shot 8 of 20 as New York shot 36.5%, lost their fifth straight and 10th in 11 games since the overtime win over Milwaukee.
After holding a 48-46 lead in a ragged first half, the Bucks took control early in the third.
Antetokounmpo scored six points in the first 4:19 of the third and gave Milwaukee a 62-54 advantage on a thunderous dunk with 7:41 left following a steal by Brogdon.
A little over two minutes later, the Bucks took their first double-digit led at 69-58 lead on a transition hoop by Antetokounmpo.
Milwaukee expanded its lead to 77-61 when Sterling Brown hit a 3-pointer with 2 1/2 minutes remaining, breaking a string of 17 straight missed 3-pointers.
A dunk by Maker, a corner 3-pointer by George Hill and another basket by Maker helped stake Milwaukee to an 84-68 lead entering the fourth.
Antetokounmpo returned with 8:25 remaining when Milwaukee held a 90-75 lead and the advantage was never below the 13 the rest of the way.