Chasing just 145 on a classic Gabba green top on Thursday, the visitors were helped by some sloppy fielding from the Heat as they won with 26 balls and eight wickets to spare.
Incumbent Test opener Marcus Harris skied a drive when still yet to score that went straight through Ben Cutting's hands into his face.
The impact split the allrounder open, but the ball then settled on Cutting's chest and he quickly threw it backwards as if to celebrate.
Harris was allowed to remain at the crease on review though, with Cutting deemed not to have had complete control of the ball and his body.
Three more dropped catches further deflated the 30,281-strong crowd, with Tom Cooper (36 from 28 balls) and Sam Harper (56 from 40) guiding them home as Cutting returned to the field sporting five stitches and a wry smile.
Brendon McCullum (50) had earlier piloted Brisbane with a steady half century off 46 balls, with an audacious scoop his only six of the night.
Chris Lynn (14 off 15) was caught on the boundary and only Cutting (20 off 10) looked comfortable as Cameron Boyce (2-17) and Usman Shinwari (3-16) combined for four troublesome overs.
The victory shot the Renegades (4-3) into third place on net run rate, while the Heat (2-4) remain in seventh.