Reserve guard George Hill chipped in 22 points while Brook Lopez and Sterling Brown each scored 14 for the Bucks, who played without All-Star forward Khris Middleton because of soreness in his left groin.
Milwaukee was unable to clinch the best record in the Eastern Conference because Toronto won earlier Monday.
D’Angelo Russell had 28 points and 10 rebounds for the Nets, who remained seventh in the East after losses by Detroit and Miami. Caris LeVert had 24 points off the bench.
Milwaukee got off to a quick start and led 35-13 lead with 1:39 left to play in the first quarter. But Brooklyn stormed back with a 28-6 spurt to go up 42-41 on DeMarre Carroll’s layup with 5:53 remaining in the half.
There were 18 lead changes in the third before Milwaukee took a 101-91 lead on a three-point play from Antetokounmpo with 10:21 to go in the fourth.
Brooklyn cut it to four after LeVert scooped up a loose ball for a layup before Antetokounmpo, who missed Sunday’s overtime loss at Atlanta with a sore ankle, led a 7-0 run with a pair of baskets to increase the lead to 121-110 with 4:11 to play.
Bucks: The Bucks earned their 26th road win, tying the 1980-81 team for the third-highest total in franchise history. . The Bucks improved to 3-0 against the Nets this season to clinch the season series. They have won the last five season series.
Nets: Joe Harris had 17 points, going 5 for 7 on 3s.
Before taking the Brooklyn coaching job, Kenny Atkinson spent three years as an assistant in Atlanta for Milwaukee’s first-year coach, Mike Budenholzer.
Now both are considered candidates for the Coach of the Year award.
Budenholzer, who won the award in 2015 after leading the Hawks to a franchise-record 60 wins, isn’t surprised at the job Atkinson has done and enjoys watching the Nets from afar.
“I would love for Kenny to be Coach of the Year,” Budenholzer said.
“I think he’s very deserving, and what he’s done here the two or three years — three years — he’s been (here), the culture, the way they compete, the way they play both ends of the floor. He’s incredibly deserving.”
Bucks: Visit the Philadelphia 76ers on Thursday night
Nets: Host the Toronto Raptors on Wednesday Night.