Butler finished with 40 points, 11 rebounds and 13 assists in the Game 3 win to cut the Heat's deficit in the championship series to 2-1. It was the third 40-point triple-double in NBA Finals history.
"I don't care about triple-doubles," said Butler, who was 14 for 20 from the field. "I don't care about none of that. I really don't. I want to win. We did that, [and] I'm happy with the outcome. ... I think we realized that we belong."
Tyler Herro and Kelly Olynyk each scored 17 points for the Heat, who squandered multiple double-digit leads throughout the game. Duncan Robinson had 13 points and Jae Crowder added 12 for Miami.
The Heat grabbed a 13-point advantage in the first quarter before the Lakers battled back and took the lead early in the second frame. Miami also had a 14-point lead after a 10-0 run to start the second half, but Los Angeles again fought back with eight straight points.
Late in the third, the Heat found themselves with a 12-point lead and appeared to be in control. The Lakers put together a 20-6 run over about five minutes to grab a 91-89 lead with 8:55 remaining in the fourth.
But the Heat reclaimed the lead and didn't look back as Butler refused to let the Heat fall into a likely insurmountable 3-0 hole. The only other time the Heat were down 2-0 in a Finals series was 2006, when Dwyane Wade led Miami all the way back.
LeBron James led the Lakers with 25 points, 10 rebounds, eight assists and two blocks. All-Star big man Anthony Davis, who was in early foul trouble, finished with 15 points and five rebounds in 33 minutes.
Game 4 of the best-of-seven series is set for Tuesday night.