Marcus Smart returned for Ime Udoka but was on limited minutes as Derrick White contributed tremendously with 14 points and five assists off the bench. Tyler Herro was still out for Miami.
The first half was low scoring, with Jayson Tatum making his first field-goal in the second quarter after a 0/6 start. Caleb Martin was excellent off the bench for Miami with his side going into the half up five.
Boston went crazy in the third quarter, creating a double-digit lead as Tatum and Brown got red hot. The match was extremely tight until a big Celtics run saw them go up 23 points at one point.
Bam Adebayo had a nice putback dunk in the first half but this was eclipsed by a monstrous slam by Brown in the fourth.
After a superb Game 3 performance, Adebayo has struggled with Robert Williams III defending him but was able to score a team-high 18 points.
Speaking of struggling, Jimmy Butler shot 22.2 per cent from the field as he made four of his 18 shots in a disappointing night. Max Strus and Kyle Lowry also failed to make a field goal, shooting zero for 15 combined.
As for the Celtics, Tatum had 22 points, 12 rebounds and nine assists as he was one assist shy of a triple double. Brown had 25 and Al Horford had 16. Williams III had three blocks and 10 rebounds on the night and shot 100 per cent, making his only two field goals.
The Heat shot a woeful 15.6 per cent from three, making seven of their 45 attempts from deep. After a slow first half, Brown had 19 points in the second period, including 13 in the fourth quarter, and Tatum had 18 after scoring four in the first half.
Boston have the chance to seal a spot in the NBA Finals on Friday night when the Heat go to the TD Garden.
Heat coach Erik Spoelstra said after the loss: "We're still alive. We have an opportunity to go up to Boston, a great crowd and make a memory we will remember for a long time"
Jaylen Brown: "It's the playoffs, if you want to do anything special that's what it's going to take, winning on the road, winning when you're not hitting shots."
Ime Udoka: "The mental stress and strain we put on some teams with our defense has worked and carried us through the playoffs," Udoka said. "Having all those bodies to continue to throw at people wears down on [them] physically and mentally … our defense travels well."
Jimmy Butler: "I got to find a way to do better."