Kevin Garnett had 24 points and 11 rebounds and Paul Pierce scored 23 points as host Boston notched its first victory in the Eastern Conference finals.
Rajon Rondo added 21 points and 10 assists and the Celtics led comfortably for most of the second half while cutting Miami’s edge in the best-of-7 series to 2-1.
LeBron James had 34 points and eight rebounds and Dwyane Wade scored 18 points for the Heat.
Boston attempts to tie the series when it hosts Game 4 on Sunday.
The Celtics led by 24 points early in the fourth quarter before Miami stated a frantic rally. Mike Miller hit three 3-pointers during a 19-4 spurt that saw the Heat pull within single digits at 91-82 on Wade’s dunk with 5:41 to play.
Boston pushed the lead back to 13 points on back-to-back baskets by Garnett and Rondo and Miami never trailed by fewer than eight points the rest of the contest.
Mario Chalmers scored 14 points and Miller added 11 for Miami.
The Celtics used a 15-0 run over the first and second quarters to turn a six-point deficit into a 37-28 lead. Miami missed nine consecutive field-goal attempts during the stretch. Pierce hit a 3-pointer to increase the lead to 14 points with 3:40 left in the half and Boston led 55-42 at intermission.
Miami’s deficit was 85-63 entering the final quarter.
GAME NOTEBOOK: The Celtics boasted a 44-32 rebounding edge. … James has eight 30-point games in the postseason, including all three contests in this series. … Garnett has 11 double-doubles in the postseason. … Heat coach Erik Spoelstra declined to say prior to the game whether or not forward Chris Bosh (lower abdominal strain) will play in Game 4. … Boston received a surprise lift from Marquis Daniels, who had nine points and five rebounds in 17 minutes after tallying just 12 points in the postseason entering the contest. … Miami was just 10 for 20 from the free-throw line after having 47 attempts in Game 3.