Wesley Matthews netted 18 points and Damian Lillard added 16 for the Blazers, who have won six of their last seven games.
The Heat led 48-43 at the break, but the Blazers began the third quarter on a 17-3 run to seize control.
Chris Kaman netted six consecutive points during the burst, which was capped on Aldridge's putback layup for a 60-51 Portland advantage midway through the frame.
Dorell Wright made a jumper at the third-quarter buzzer to stake the Blazers to a 76-64 margin going into the fourth.
Portland outscored Miami 33-16 in the third.
Matthews and Allen Crabbe hit consecutive 3-pointers prior to Matthews' alley- oop layup, which upped the cushion to 86-69.
Portland, which trailed 23-18 following a period of play, led by as many as 23 down the stretch.