Butler was outstanding, playing through a knee issue that has plagued him in the Conference Finals, to shoot 16 of 29 from the field with nine rebounds, eight assists and four steals.
The 32-year-old small forward had only managed eight, six and 13 points in his past three games, rising to force a Game 7 back in Miami with the series tied 3-3.
“I got a phone call and text message from D-Wade earlier today and he was telling me I can do this,” Butler told ESPN after the game.
“Knee is banged up, but nobody cares. Go out there and continue to build your legacy.
“That meant the world to me, so I appreciate you, D-Wade.”
Kyle Lowry contributed with 18 points including four three-pointers, while Max Strus found his range finally, with 13 points including three triples.
“It’s incredible to have a guy like him next to me,” Lowry said about Butler. “I’ve played with some great players, and he’s one of the best.”
The winner of Game 7 will take on the Golden State Warriors in the NBA Finals.
Heat head coach Erik Spoelstra said: “This is the way it should be, with these two teams. It should have gone seven games.
“I’m just really thrilled that our group gets an opportunity to compete in a Game 7 in front of our home crowd.”