Khris Middleton had 20 points, nine assists and eight boards for Milwaukee, which entered four games ahead of the Detroit Pistons for the No. 8 seed. With four games to play, the Bucks could finish as high as the No. 6 seed.
Jaylen Brown scored 24 points and Jayson Tatum added 20 as the Celtics' six-game winning streak ended. Boston remains two games behind East-leading Toronto ahead of a Wednesday matchup with the Raptors.
With star Kyrie Irving and defensive centerpiece Marcus Smart already out with injuries, the Celtics also played without Terry Rozier (left ankle sprain) and Shane Larkin (illnesss). Kadeem Allen started at point guard and was held to two points.
Eric Bledsoe had 18 points and Jabari Parker scored 12 for the Bucks, who shot an efficient 54.4 percent (43 of 79) for the game and outrebounded the Celtics 41-37.
Al Horford contributed 15 points, Marcus Morris scored 13 and Aron Baynes had 12 for Boston.
Milwaukee was up 79-71 heading into the fourth quarter before Boston came within five going into the final minute.
Bledsoe's finger roll with 36 seconds left was answered by five straight points from Tatum, whose dunk after a Middleton turnover with 24.2 seconds to play brought the Celtics within 103-100.
Antetokounmpo hit two free throws and Middleton made one of two to seal the victory.
Tatum's 3-pointer at the second-quarter buzzer set a new franchise record for 3s in a rookie season (102) and brought the Celtics within 58-56 at halftime.
Boston led 31-26 after one quarter.
The Celtics visit the Raptors on Wednesday. Milwaukee hosts Brooklyn on Thursday.
--Field Level Media
Boston | Milwaukee | |
Jaylen Brown 24 | Scoring | Giannis Antetokounmpo 29 |
Al Horford 5 | Assists | Khris Middleton 9 |
Greg Monroe 10 | Rebounds | Giannis Antetokounmpo 11 |
Jayson Tatum 7 | Free Throws Made | Giannis Antetokounmpo 7 |
Jayson Tatum 3 | Steals | Khris Middleton 3 |
Kadeem Allen 1 | Blocks | John Henson 3 |
Team | Points | FG% | 3PM-3PA | FTM-FTA | Assists | Rebounds | Blocks | Steals | Turnovers |
Boston | 102 | 46.9 | 7-23 | 19-24 | 19 | 37 | 6 | 10 | 17 |
Milwaukee | 106 | 54.4 | 5-20 | 15-21 | 27 | 41 | 5 | 6 | 15 |