Vincent made 11 of 14 shots from the floor -- including 6 of 9 from 3-point range -- and Duncan Robinson and Caleb Martin scored 22 and 18 points off the bench, respectively.
Jimmy Butler collected 16 points, eight rebounds and six assists for eighth-seeded Miami, which shot a blistering 56.8 percent from the field (46 of 81) and 54.3 percent from 3-point range (19 of 35). The Heat improved to 6-0 at home in the playoffs ahead of Game 4 of the best-of-seven series on Tuesday in Miami
Boston's Jayson Tatum recorded 14 points and 10 rebounds and Jaylen Brown scored 12 points, although the pair combined to make just 12 of 35 shots from the floor and 1 of 14 from 3-point range.
The Celtics have their backs against the wall. No team in NBA history has overcome a 3-0 deficit to win a series
Boston whittled a 22-point deficit down to 12 at 61-49 after Marcus Smart converted a three-point play to start the third quarter. Miami answered with a 28-9 run to seize control of the game, highlighted by a pair of 3-pointers by Vincent.
The Heat carried a 93-63 lead into the fourth quarter before both teams opted to rest their stars. Vincent sandwiched 3-pointers around a three-point play and Robinson converted from beyond the arc to extend Miami's advantage to 112-83 with 4:43 to play
Miami claimed a 61-46 lead at halftime after shooting a sizzling 57.5 percent from the floor (23 of 40) and 42.9 percent from 3-point range (9 of 21). Martin sank a trio of 3-pointers to highlight his 11-point performance, while Robinson and Vincent each made a pair from beyond the arc to finish with 10 points apiece.
Miami's Kevin Love scored five quick points to start the game before exiting after five minutes with an ankle injury. He did not return.
--Field Level Media