The Heat controlled the game after halftime, building the lead to 17 early in the fourth quarter as both teams played their reserves down the stretch.
Memphis battled back within 94-91 on a jumper by Jon Leuer near the 4-minute mark, but the Grizzlies got no closer.
Leuer led the Grizzlies with 21 points, while Vince Carter added 13, including connecting on all three of his 3-pointers. Zach Randolph was the only Memphis starter in double figures with 12 points. Rookie Jordan Adams also had 12 points.