The Celtics scored 32 points on 21 Milwaukee turnovers.
"We had more turnovers than assists. It's tough to win like that," said Bucks center Zaza Pachulia, who had eight points and eight rebounds starting in place of injured Larry Sanders.
Bucks coach Larry Drew was disappointed about his team's lack of energy in the game-changing fourth quarter.
"(The Celtics) played (Sunday) night, but they seemed to be playing with more energy than we did," Drew said.
The Celtics held a 49-46 advantage at the half despite shooting just 40 percent. Brandon Bass led the way with 12 points. Knight had 14 first-half points for the Bucks, who shot 44 percent. The Celtics had 11 second-chance points compared to just one for the Bucks.
It was back and forth through the first two quarters with 10 lead changes and six ties.
Boston held a 26-24 lead after the first quarter, sparked by Bass, who had all 12 of his first-half points in the quarter.
"He just manhandled us down on the block. He's a bruiser," Drew said. "He loves to catch the ball down low. We didn't accept the challenge on Bass."
Boston shot 48 percent for the game, compared with 43 percent for Milwaukee.
Notes: Sanders was diagnosed with a fractured orbital bone in his right eye. He was injured when he was elbowed by James Harden in Saturday's game against the Houston Rockets. He's expected to be out at least through the All-Star break, Drew said. ... The Bucks also were without Caron Butler (ankle), Ersan Ilyasova (back) and O.J. Mayo (illness). Luke Ridnour (back) and Ekpe Udoh (ankle) returned to the lineup. ... Celtics G Rajon Rondo sat out after logging a season-high 37 minutes Sunday. He's been limited from playing in back-to-back games as he recovers from ACL surgery. "I think he'll be playing back-to-backs very soon," Stevens said. ... Celtics' starting G Avery Bradley (sprained right ankle) also was out of the lineup. He's scheduled to undergo an MRI on Tuesday.