Antetokounmpo had 27 points and Khris Middleton had 23 to power Milwaukee, which lost the first two games of its Eastern Conference quarterfinals series in Boston before coming to life with two home wins.
Boston's Marcus Morris missed a fadeaway jumper at the buzzer that would have tied it.
Jaylen Brown set another playoff career high with 34 points to lead the Celtics. Brown set his previous playoff highs of 20 and 30 in the first two games of the series. Jayson Tatum added 21 points and both Morris and Al Horford scored 13.
Boston has never lost a playoff series when leading 2-0. Milwaukee, which won Game 3 116-92, has never won a series after starting in an 0-2 hole.
Game 5 is Tuesday in Boston.
The Bucks recorded 14 blocks, five of which came from Thon Maker.
Milwaukee's John Henson (back) missed his second straight game. Tyler Zeller again started, but it was backup center Maker who benefitted most from the minutes created by Henson's absence.
After scoring 14 points with five rebounds and five blocks in Game 2, Maker had eight points, two rebounds and five blocks Sunday.
Morris' driving layup with 9:03 remaining tied the game at 75, but the Bucks regained their edge and went up by six on an Antetokounmpo jumper with 3:22 to play.
A 3-pointer by Brown at the 1:29 mark brought the Celtics within one and Tatum's jumper with 52.4 seconds left capped a 10-4 run to put Boston ahead 100-99, its first lead since being up 14-13 in the first quarter.
Brogdon restored the Bucks' advantage with his corner three with 33.5 seconds remaining. Horford was fouled by Maker on a driving dunk attempt with 29.6 left, and he made both free throws to tie it at 102.
After trailing by as many as 28 points in its Game 3 loss, Boston again fell behind by 20 in the third quarter. But the Celtics rallied late in the third to trim their deficit to 75-67 entering the fourth.
Milwaukee led 51-35 at halftime, marking the second straight game in which it held Boston to 35 first-half points. The Bucks trailed for most of the first before ending the quarter on a 22-2 surge to go up 27-14.
--Field Level Media
Boston | Milwaukee | |
Jaylen Brown 34 | Scoring | Giannis Antetokounmpo 27 |
Terry Rozier 8 | Assists | Giannis Antetokounmpo 5 |
Aron Baynes 11 | Rebounds | Giannis Antetokounmpo 7 |
Al Horford 5 | Free Throws Made | Khris Middleton 4 |
Jaylen Brown 3 | Steals | Khris Middleton 2 |
Al Horford 2 | Blocks | Thon Maker 5 |
Team | Points | FG% | 3PM-3PA | FTM-FTA | Assists | Rebounds | Blocks | Steals | Turnovers |
Boston | 102 | 41.4 | 10-29 | 20-25 | 22 | 43 | 3 | 6 | 9 |
Milwaukee | 104 | 52.1 | 10-23 | 18-24 | 24 | 36 | 14 | 7 | 10 |