Justise Winslow, Miami's recently converted point guard, added 13 points and 11 assists, a game high and career high. "We're trying to continue to get better", said Wade, who helped the Heat even their record at 20-20.
The Boston Celtics have hit the midway point of the season and are now 25-16, good for fifth in the Eastern Conference.
As seen in the video footage embedded below, the two exchanged words near the bench before Morris shoved Brown and Marcus Smart had to step in.
Miami led 61-43 at halftime with Derrick Jones draining a three-pointer on the buzzer from just inside the half-court line, one of 18 long-range shots that hit the target.
The Green trailed by as much as 26 points in the third quarter, but pulled within eight points late in the quarter before the Heat pulled away in the fourth.
Despite some early struggles, the Celtics are still the fifth seed in the East, and 4.5 games out of first at 25-15. Boston has now lost three straight to Miami, the first time that's happened since 2012.
The Celtics will have an opportunity to put the double-digit loss behind them and get back in the win column on Saturday night, when they square off against the Magic. Boston is 7-2 in its last nine games against Orlando.
Heat: It was Miami's 400th consecutive home sellout. Brown was benched the rest of the half and did not re-enter until just before the end of the third quarter.
The Boston Celtics have dealt with a few ups and downs through the start of the 2018-19 National Basketball Association season.
Boston and Miami didn't play each other in 2018 - the last meeting between the clubs, before Thursday, came on December 20, 2017.