Bam Adebayo scored 20 points, Duncan Robinson added 20, and Tyler Herro finished with 18 as Miami improved to 23-24.
"It's a great feeling (to win after) anytime you drop any in a row, let alone six in a row," Robinson said. "We were struggling ,so it's certainly nice to just get this one."
Julius Randle led New York with 22 points. Derrick Rose scored 16 points and Immanuel Quickley added 12, both off the bench, as the Knicks had their three-game winning streak halted and slipped to 24-23.
"We'll bounce back," Randle said.
The franchises engaged in an epic rivalry beginning in 1995 and culminating in 2000. Over the course of 20 regular-season games and 24 playoff games in back-to-back-to-back-to-back seasons, those Heat and Knicks teams redefined tough, passionate, emotional, defensive-oriented, compelling basketball.
While it is to be determined whether the teams will compete in the meaningful games this season, the final regular-season matchup between New York and Miami began as a possession-by-possession contest.
New York led 43-36 at halftime thanks to a strong defensive performance in the opening quarters. The Knicks limited the Heat to 33.3% (14 for 42) shooting from the field, 21.1% (4 for 19) from long range and forced six turnovers.
"It (was) like a playoff game environment," Knicks swingman RJ Barrett said. "That's what we're looking forward to, somewhere we want to get to. So it was good to have."
But the Knicks could not build on their advantage and trailed 75-64 entering the fourth quarter. Miami scored 39 points in the third, including 14 by Butler.
"As a young guy, it's amazing for me to watch," Herro said of Butler. "I think at any point throughout the game we all know he can turn it on."
New York outscored Miami 14-9 over the first 6:23 of the fourth, cutting the Heat's lead to 86-78. But Miami scored 12 of the final 22 points to seal the win.
Miami swept the regular-season series.
Heat: Prior to the game, Miami coach Erik Spoelstra offered updates on guards Goran Dragic and Kendrick Nunn. Dragic played in his first game since Miami's 137-110 loss to Indiana on March 19. He had sat out the four games following the loss to the Pacers with back spasms. "He felt good," Spoelstra said before the game. "He was able to go through the full workout. We practiced (Sunday), he was able to go through the shootaround this morning. He's ready to go." Nunn did not play against the Knicks with what Spoelstra diagnosed as "a sprained ankle." Spoelstra added Nunn "is moving around" and is still traveling with the team.
Knicks: Prior to the game, the team announced center Mitchell Robinson underwent "successful surgery ... to repair a fractured fifth metatarsal in his right foot at the Hospital for Special Surgery." Head coach Tom Thibodeau, during his pregame availability with reporters said he had yet to meet with team doctors to discuss a timeline for Robinson to return to the team. ... Mike Woodson, who had served as an assistant coach to Thibodeau, was introduced as the new men's head basketball coach at the University of Indiana. "He's a great coach," Taj Gibson said about Woodson following the Knicks' shootaround Monday. "He's a long-time teacher." Franchise legend Walt Frazier turned 76 Monday. Frazier, who is in the Hall of Fame and is the Knicks' color analyst for MSG Network, was feted with a video tribute and a standing ovation during a timeout.
Heat: Visit Indiana on Wednesday night.
Knicks: Visit Minnesota on Wednesday night.
Bam a force in the paint on back-to-back possessions
Bam Adebayo drives through the paint for an and-1 bucket and then hits a jumper over Nerlens Noel.