The Celtics led by 29 in the second half before Phoenix scored the last nine points in the third quarter and the first nine of the fourth. But the Suns, who had won four straight, never got closer than eight points.
Aaron Brooks scored 17 points, former Boston College star Jared Dudley had 15 and fellow reserve Marcin Gortat had 13 points and 13 rebounds. The Suns played the last 17 minutes without Vince Carter and Channing Frye, who banged heads and left the game.
The game was the Boston debut of the new-look Celtics, who acquired Jeff Green and Nenad Krstic at the trading deadline and added Troy Murphy earlier Wednesday.
Krstic had 13 points, Green scored six in 17 minutes and Murphy scored one point in 14 minutes.
It was the first time the teams played since Garnett poked Frye in the lower groin on Jan. 28, when the Suns won 88-71. That was Phoenix's third straight victory over Boston.
But the defending Eastern Conference champions snapped that streak, winning for the sixth time in seven games and moving 1 1/2 games ahead of the Miami Heat in the race for the best record in the East.
The Suns got a scare when Frye and Carter banged heads with 4:53 left in the third quarter. Frye got up after a minute or two, but Carter stayed on the court longer and eventually walked off, rubbing his head and clearly unsteady on his feet.
The team said Frye had a bruised eye and Carter had a cut on his mouth. Neither returned.
Garnett scored 12 points in the first quarter as the Celtics shot 60 percent — getting 18 points in the paint — and jumped to a 13-point lead. He had 18 at the half, when Boston led 62-42.
The Celtics led by as many as 29 in the quarter, and held a 91-63 lead with 2 minutes left in the quarter before Dudley hit back-to-back 3-pointers and then a pair of free throws. Gortat made one of two foul shots to end the quarter, then Phoenix scored the first nine points in the fourth to make it a 10-point game.
It was 93-85 when Rondo made a jumper and then assisted on Krstic's layup to make it a 12-point game.
Notes
Murphy signed earlier Wednesday. He is the first Murphy to wear the shamrock since Dick Murphy played seven games in the NBA's inaugural season, 1946-47. … Pierce and Steve Nash are neck-and-neck for the top 10 all-time in 3-pointers. Pierce did not make any in the game and finished with 1,550 in his career; Nash hit one and has 1,547. Ray Allen is the all-time leader; he was 4-for-6 on Wednesday and has 2,578. … Phoenix's bench outstcored its starters 63-40 and outscored Boston's bench 63-23. … Boston's Glen Davis appeared to hurt his left knee, which was already wrapped in a brace, on a dunk in the final minute. … Garnett was given a technical foul with 17 seconds left.