Brown eclipsed his previous playoff high of 20 in the Celtics' 113-107 overtime victory in Game 1 on Sunday. Terry Rozier finished with 23 points, Marcus Morris had 18 and Al Horford added 16 for Boston.
Giannis Antetokounmpo paced Milwaukee with 30 points, nine rebounds and eight assists after leading all scorers with 35 in Game 1. Khris Middleton added 25 points for the Bucks, who hope to avoid their fourth first-round playoff exit in six years.
Game 3 is Friday night in Milwaukee.
Boston shot 53.3 percent (48 of 90) and each team grabbed 38 rebounds.
"What more can you ask for?" Brown said, according to NBCsports.com. "Everybody's writing us off. They're saying that we're too young, and we're not even listening."
Eric Bledsoe and John Henson scored 12 apiece, Shabazz Muhammad had 11 and Malcolm Brogdon added 10 as the Bucks lost despite shooting 59.7 percent (46 of 77).
Boston's Greg Monroe was questionable with an illness, but played and had 12 points and four rebounds against his old team.
Shane Larkin's buzzer-beating 3-pointer had Boston up 90-75 entering the fourth quarter.
The Celtics led by as many as 20 in the fourth.
Boston led 60-51 at halftime and stretched its advantage to as many as 16 in the third on Larkin's reverse layup with 4:01 to play.
Down 33-22 after the first, the Bucks used a 13-2 run to tie the game at 35 on Muhammad's 3-pointer with 8:27 left in the second.
The Celtics answered with a 7-0 surge and had the lead back up to nine at halftime.
After scoring 31 points in Game 1, Middleton was held scoreless until his jumper broke the Boston run with 6:17 before the break.
Before the game, Celtics guard Marcus Smart revealed his mother recently had been diagnosed with cancer. Smart is recovering from right thumb surgery, but said his mother's wishes were that he remain with the team.
--Field Level Media
Milwaukee | Boston | |
Giannis Antetokounmpo 30 | Scoring | Jaylen Brown 30 |
Giannis Antetokounmpo 8 | Assists | Terry Rozier 8 |
Giannis Antetokounmpo 9 | Rebounds | Jayson Tatum 7 |
Giannis Antetokounmpo 4 | Free Throws Made | Terry Rozier 4 |
Giannis Antetokounmpo 1 | Steals | Jayson Tatum 4 |
Giannis Antetokounmpo 1 | Blocks | Aron Baynes 2 |
Team | Points | FG% | 3PM-3PA | FTM-FTA | Assists | Rebounds | Blocks | Steals | Turnovers |
Milwaukee | 106 | 59.7 | 7-17 | 7-17 | 19 | 38 | 4 | 3 | 15 |
Boston | 120 | 53.3 | 13-31 | 11-18 | 24 | 38 | 6 | 10 | 7 |