Celtics forward Gordon Hayward saw Brown cut to the basket in front of Antetokounmpo and delivered a pinpoint pass. Brown jumped and threw down a two-handed slam over Antetokounmpo, who extended his right arm but failed to block the attempt.
Brown had 19 points on 8-of-14 shooting with four rebounds against the Bucks.
The Celtics earned a 112-90 win over Milwaukee in the first game of their Eastern Conference semifinal series. Boston center Al Horford, who blocked Antetokounmpo twice in a row, and the Celtics contained the Bucks and their star forward.
Antetokounmpo had 22 points on 7-of-21 shooting with eight rebounds and two assists. Khris Middleton had a double-double with 16 points and 10 rebounds.
Celtics point guard Kyrie Irving had 26 points, 11 assists and seven boards. Horford had 20 points and 11 rebounds.
The Bucks host the Celtics in Game 2 Tuesday night.