Julius Randle had 29 points, 14 rebounds and seven assists, Elfrid Payton scored 27 points in his best game as a Knick, and New York led by as much as 28 against the team that had the best record in the NBA the previous two seasons.
The Knicks were among the NBA's worst during that time but are hoping for a turnaround under Thibodeau, the former Coach of the Year who engineered comebacks in Chicago and Minnesota.
''As long as we're putting the work into it, we'll get better,'' Thibodeau said.
The Knicks opened his tenure by hanging with Indiana and Philadelphia for a half before those teams pulled away in the final two quarters.
This time, they used a 16-2 run late in the first half to open a 61-43 lead, then got 12 points apiece from Randle and Payton in the third to make it a 21-point lead heading to the fourth. The Knicks opened the final period with seven straight points for a 103-75 bulge.
''We put good halves together against Indiana and last night,'' Randle said. ''We've just got to put the second half, full game together and that's what we did tonight.''
Giannis Antetokounmpo had 27 points and 13 rebounds for the Bucks, who were coming off a 39-point trouncing of Golden State on Christmas and looking to build momentum before playing two straight games in Miami against the team that eliminated them in the Eastern Conference semifinals.
Teams are sometimes being scheduled for consecutive road games in one city this season as a way to reduce traveling during the coronavirus pandemic.
But after going 20 for 37 on 3-pointers Friday, the Bucks were 7 for 38 (18%) behind the arc against the Knicks. They also allowed the Knicks to shoot 54% from the field and 59% from 3-point range.
''They had a great night shooting and we've probably got be a lot better defensively,'' Bucks coach Mike Budenholzer said.
Alec Burks scored 18 points and RJ Barrett bounced back from a poor performance against Philadelphia with 17 as the Knicks had plenty of offense even without injured rookies Obi Toppin (calf) and Immanuel Quickley (hip) for the second straight game.
Frank Ntilikina had 12 points on 4-for-4 shooting from 3-point range, making New York's point guards 7 for 7 behind the arc. Payton made all three of his attempts as part of a 12-for-16 night overall.
''I think we all know we have to be better,'' Bucks reserve Bobby Portis said.
Bucks: Khris Middleton scored 22 points. ... Jrue Holiday, who had 64% of his shots in his first two games with the Bucks, shot 4 for 10 for eight points. ... Portis, who played for the Knicks last season, had 17 points.
Knicks: Thibodeau said G Austin Rivers, who hasn't played this season because of a sore right groin, has made progress and would go through the contact portion of practice for the first time on Monday. ... Thibodeau said he expected Quickley to be able to jump right back in when he was cleared, but thought Toppin would need more time because of the nature of his injury prevents him from doing much while he's out.
Payton's best game last season, his first in New York, was 20 points. He opened 2020-21 by going 3 for 13 in two games.
Bucks: Play two straight games in Miami on Tuesday and Wednesday.
Knicks: Visit Cleveland on Tuesday to start a four-game trip.
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