The Heat beat the Celtics 125-113 in Game 6 to take the Eastern Conference finals with Butler posting 22 points with eight assists.
Adebayo had 32 points and 14 rebounds.
The Celtics took a 96-90 lead with 9:15 left in the fourth quarter. But Butler and Adebayo then sparked a run that led the Heat to their first Finals appearance since 2014.
“One more to go,” Butler said in the postgame trophy ceremony. “But if anyone can do it, we can do it.”