In a match where tempers frayed between Australian one-day teammates Clint McKay and Dan Christian, the Heat (5-171) ended the Stars' four-match winning streak with a spirited comeback on Thursday night.
Super slinger Malinga continued his destructive BBL form with an amazing 3-0 from his first 10 balls to have the home side staring at a sub-par total of 140.
But thanks largely to Shane Warne's rusty fielding and Chris Lynn's late-innings hitting, Brisbane set a respectable target which couldn't be reined in.
Dropped by Warne, his second embarrassing miss in the field, Lynn (26 not out) then helped peel off 17 runs off the final over by Malinga (3-26).
Heat skipper James Hopes followed his 49 with the bat to take 3-28 with the ball in a man-of-the-match performance which tormented the Stars' international-quality line-up.
Sri Lankan all-rounder Thisara Perera, in his last match for Brisbane, chimed in with 3-18 as the visitors were kept to 9-147.
A big crowd of 24,500 - the biggest of the season at the Gabba - lapped up the result which moves the Heat to fifth on the table with 3-3 record.
The Stars (4-2) remain in second place on eight points.
Emotions boiled over in the Heat innings when McKay and Christian engaged in a heated exchange, trading insults from close quarters, after the batsman prevented a run-out with his running line.
Warne, who won the toss and bowled first, showed his own lack of confidence in the field by calling Luke Wright to take a skied ball from Perera that landed where the 43-year-old had been standing.
Warne admitted the Stars let the home side off the hook following their impressive start.
"It was a little disappointing tonight in all three departments - our fielding and our bowling, we didn't quite get it right, and in our batting we lost wickets at crucial times," he said.
"Our last four overs went for 52 and 170 was a par score here as it was a really good wicket so we thought we could chase it down."
Hopes, who set the foundations with a two-paced 63-run second-wicket stand with surprise No.3 Chris Hartley, felt the Heat had some momentum after winning just one of their first four matches.
"It's a funny thing with our side, we tend to play our best when our backs are to the wall and we have to lose a few first to get on a winning streak," he said.