Game 6 of the series is Sunday night. The Lakers still hold a 3-2 lead in the best-of-seven series.
"This one was a little bit of luck that Danny Green missed that shot at the top of the key," Butler said.
Heat sharpshooter Duncan Robinson had arguably his best game of the postseason with 26 points on 7-of-13 shooting from 3-point range. Kendrick Nunn had 14 points, while Bam Adebayo chipped in 13 points, four rebounds and four assists.
Jae Crowder scored 11 points, and Tyler Herro added 12 for the Heat.
LeBron James had 40 points, 13 rebounds, seven assists and three steals for the Lakers. Anthony Davis, who was hampered by a foot injury for much of the game, notched 28 points, 12 rebounds and three blocks. Kentavious Caldwell-Pope added 16 points.
Robinson's 3-pointer with 3:13 remaining in the fourth quarter gave the Heat a two-point lead and started a stretch where the next nine scoring possessions from either side resulted in a tie or lead change.
Butler was fouled with 46.7 seconds left and made both free throws for a one-point lead. Davis answered with a putback with 21.8 seconds remaining to put the Lakers back on top.
Heat head coach Erik Spoelstra used his last timeout before the team's next possession, giving Butler a little extra rest. Butler then drove the lane and drew another foul, sinking both foul shots for a 109-108 lead.
The Lakers -- seeking their first NBA championship in a decade -- called a timeout in preparation for the possible title-winning shot. James drove for a layup but kicked the ball out to Green for a wide-open 3-pointer, which clanged off the rim. Herro finished off the game with two free throws.