The top-seeded Celtics made 22 of 49 attempts from three-point range (44.9%). All eight Celtics who saw playing time made a three-point attempt. Eighth-seeded Miami was 12 of 37 (32.4%) from three-point range.
Derrick White (20 points), Kristaps Porzingis (18), Jaylen Brown (17), Sam Hauser (12 ) and Al Horford (10 ) also scored in double figures for Boston, which won all three meetings with Miami during the regular season.
Miami's Bam Adebayo led all scorers with 24 points. Delon Wright came off the bench to score 17 for the Heat, and Jaime Jaquez Jr added 16.
Miami used a 26-7 run to pull within 103-88, with 3:58 remaining, but the Heat failed to get any closer than 14 points in the final minutes.
Boston scored the game's first 14 points. Miami didn't get on the scoreboard until Adebayo made a jumper with 8:44 left in the first quarter. Boston led 17-2 with 8:26 to play in the quarter, but the Heat outscored the Celtics 19-9 the rest of the way to make it a 26-21 game after 12 minutes.
The Celtics had their largest lead of the first half at 18 points after Tatum capped a 9-0 run with two free throws that put Boston up 48-30 with 7:03 to play before the break. The Celtics made 12 of 30 attempts from three-point range in the first two quarters and led 60-45 at half-time.
Boston held Miami to 14 points in the third quarter. The Celtics went on a 15-0 run and had an 89-57 advantage when White made a three-pointer with 31.9 seconds left in the third. Boston made 7 of 13 attempts from distance in the quarter.
Game Two in the best-of-seven series is Wednesday in Boston.
