The Knicks had lost their previous nine games against Milwaukee, including a 130-111 decision on Saturday.
That followed a pair of comfortable Bucks wins earlier this season, but Brunson's effort, along with a solid defensive showing, saw the Knicks come out on top in the first game of the NBA's Christmas Day slate.
The match-ups also include Golden State at the reigning champion Denver Nuggets, the Boston Celtics at the Los Angeles Lakers, Philadelphia at Miami and Dallas at Phoenix.
"I'm just happy the way we played today, we kept fighting," Brunson said after the Bucks cut a 14-point deficit to four midway through the third quarter before the Knicks pulled away again.
"They made a run but we stayed poised," Brunson said. "You've got to give them a lot of credit, they're a hell of a team so I'm just happy we got away with a win."
Julius Randle scored 24 points and grabbed nine rebounds, RJ Barrett bounced back from a disappointing showing on Saturday to score 21 points and Immanuel Quickley added 20 off the bench for the Knicks.
Giannis Antetokounmpo and Damian Lillard each scored 32 points apiece for Milwaukee.
Antetokounmpo added 13 rebounds but the Bucks never led after the first quarter.
"I thought they out-competed us today for the most part," Bucks coach Adrian Griffin said. "Offensively we got some good looks but we just couldn't knock 'em down. And when you're on the road and you get clean looks you've got to knock them down.
"I think we missed quite a few at the rim," he added. "I think it took some of the air out of us."
