Dragic, who dropped a game-high 30 points, hit a leaner in the lane to put the Heat up by one with 15.2 seconds remaining in regulation.
The Lakers (31-38) had one last chance to seal the deal, but Isaiah Thomas' contested step-back jumper fell short, meaning L.A. dropped its second straight game.
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Thomas shot 1-of-9 from the field off the bench on what proved to be less than a banner night for Lakers point guards.
Beyond Thomas' discouraging five-point showing, Lonzo Ball continued to be plagued by jump-shooting woes.
In 38 minutes, 2017's No. 2 overall pick finished with nine points on 4-15 shooting (1-of-3 from three), eight rebounds, eight assists, two steals and three turnovers.
Ball has now shot 11-of-48 (23 percent) from the field over his past four games and is 4-of-24 from three during that same stretch.
"We need Zo taking and making more shots," head coach Luke Walton said before the loss, according to Lakers Nation's Harrison Faigen. "A lot of the shots are open looks, and we want him taking them with no hesitation. We want him stepping up, and we know that he can knock them down. He knows he can knock them down. So we're confident that he'll start hitting more."
Lonzo and Co. will have a few days off before they begin a four-game road trip Monday against the Indiana Pacers. The Lakers will be eyeing a series sweep after they defeated the Pacers by 13 on Jan. 19.
The Heat (37-33) are also scheduled to return to the floor Monday, when they are scheduled to host the Denver Nuggets at American Airlines Arena.