Khris Middleton and Malcolm Brogdon each scored 16 and both Jabari Parker and Eric Bledsoe finished with nine for Milwaukee, which bounced back from a 92-87 loss in Boston on Tuesday in Game 5.
"We said as a team before the game that we were going to play hard, we were going to win this game no matter what, and that the season's not going to end here," Antetokounmpo told TNT after the game.
Jayson Tatum had 22 points and Terry Rozier contributed 18 with seven rebounds and five assists for the Celtics. Jaylen Brown scored 14 points, Marcus Morris added 12 and Al Horford totaled 10 points and 10 rebounds for Boston.
The home team has won every game so far in the best-of-seven series.
Game 7 is Saturday night in Boston. The winner will face the Philadelphia 76ers in the conference semifinals.
The Celtics are 22-8 in Game 7s, while the Bucks are 2-7.
Boston is 35-0 all-time in playoff series when winning the first two games. Milwaukee has never won in 17 prior series when trailing 0-2.
After trailing by 14 points, the Celtics came back to tie the game at 61 on Tatum's cutting layup with 4:21 to play in the third quarter. However, the Bucks ended the period on a 13-4 run to go up 74-65 after three.
Morris' 3-pointer with 7:13 remaining had the Celtics within 80-72, but the visitors came no closer as the Bucks built the lead back up to double digits.
Milwaukee led 48-39 at halftime.
Boston's Marcus Smart appeared to hurt his right hand after being fouled by Thon Maker with 4:17 to play in the first quarter. It was Smart's second game back from right thumb surgery that sidelined him for the last 15 regular-season games and the first four playoff games.
However, Smart remained in the game and finished with six points in 26 minutes.
--Field Level Media
Boston | Milwaukee | |
Jayson Tatum 22 | Scoring | Giannis Antetokounmpo 31 |
Terry Rozier 5 | Assists | Matthew Dellavedova 6 |
Al Horford 10 | Rebounds | Giannis Antetokounmpo 14 |
Jayson Tatum 8 | Free Throws Made | Giannis Antetokounmpo 5 |
Jayson Tatum 2 | Steals | Giannis Antetokounmpo 1 |
Al Horford 2 | Blocks | Eric Bledsoe 1 |
Team | Points | FG% | 3PM-3PA | FTM-FTA | Assists | Rebounds | Blocks | Steals | Turnovers |
Boston | 86 | 37.0 | 10-36 | 16-19 | 18 | 39 | 3 | 3 | 9 |
Milwaukee | 97 | 50.7 | 8-26 | 13-21 | 19 | 48 | 3 | 6 | 11 |