The Heat trailed for most of the game until Allen took over, scoring the game's final seven points to finish with 17 and five rebounds.
Dwyane Wade helped out with 18 points and seven boards for Miami.
The Cavaliers lost their second straight since despite 16 points each from Jeremy Pargo and Dion Waiters.
Ray Liotta sues skin care company over use of likeness
Kim Kardashian, Kanye West reportedly set wedding date