Jayson Tatum added 20 points for Boston, which will face the Philadelphia 76ers in the Eastern Conference semifinals starting Monday night in Boston.
Khris Middleton had 32 to lead Milwaukee, which was denied its first playoff series victory since the 2000-01 season. Despite forcing a seventh game, the Bucks dropped to 0-18 in team history when trailing 0-2 in the playoffs.
Eric Bledsoe scored 23 points and Giannis Antetokounmpo had 22 points, nine rebounds and five assists for Milwaukee.
"We thought we were the better team, but unfortunately we cannot move to the second round," Antentokounmpo said when asked if the Bucks took pride in pushing the series to seven games. "It was a good series, but we thought we were the better team.
The Celtics played in their NBA-record 31st Game 7, improving to 23-8. The Bucks dropped to 2-8 lifetime in decisive seventh games.
"We're on edge. Everything's on the line, and I felt like our players, we felt that," Horford told NBC Sports Boston after the game. "We've been doing this all year. Guys were coming together at different times and making plays, and that's what we did tonight."
The home team won every game of the best-of-seven series.
Boston's Jaylen Brown exited the game late in the first half with a sore right hamstring. He was spotted riding an exercise bicycle at the start of the second half and was later deemed available to return but did not. Brown finished with two points.
Bledsoe's basket cut Boston's lead to 54-51 with 9:33 remaining in the third quarter. Horford scored six of the Celtics' next 11 points, including an alley-oop dunk from Marcus Smart, to put the hosts up 65-55.
Tatum's 3-pointer stretched the Boston advantage to 16 late in the quarter before two Antetokounmpo free throws made it 81-67 after three.
The Bucks never got within single digits after that, and the Celtics led by as many as 19.
Boston led 50-42 at halftime.
Bledsoe's turnaround hook shot capped a 13-2 run to bring Milwaukee within 32-30 with 8:47 left in the second, but the Celtics were soon back up by double digits and went in to the locker room up by eight.
Aron Baynes' buzzer-beating jumper had Boston ahead 30-17 after the first.
--Field Level Media
Milwaukee | Boston | |
Khris Middleton 32 | Scoring | Al Horford 26 |
Giannis Antetokounmpo 5 | Assists | Terry Rozier 9 |
Giannis Antetokounmpo 9 | Rebounds | Al Horford 8 |
Giannis Antetokounmpo 7 | Free Throws Made | Jayson Tatum 5 |
Jabari Parker 2 | Steals | Marcus Smart 3 |
Giannis Antetokounmpo 1 | Blocks | Al Horford 1 |
Team | Points | FG% | 3PM-3PA | FTM-FTA | Assists | Rebounds | Blocks | Steals | Turnovers |
Milwaukee | 96 | 47.3 | 9-27 | 17-18 | 21 | 32 | 3 | 4 | 16 |
Boston | 112 | 53.6 | 9-26 | 13-21 | 28 | 42 | 4 | 9 | 15 |