After winning the toss on a bouncy Gabba wicket, Brisbane posted 7-144 off their 20 overs which the Stars, missing Australian one-day players Clint McKay, James Faulkner and Glenn Maxwell, ran down with just two balls to spare.
The only undefeated side in the Big Bash League were made to work hard for their sixth win with Brisbane coming back from the brink time after time.
The Heat were left reeling at 5-53 in just the 10th over and were then battling with the ball as the Stars raced to 0-43 off just five overs.
But a defiant batting stand by Daniel Christian (68 not out off 48 balls) and a captain's performance with the ball by James Hopes (3-23) kept the Heat in the match.
Lusty hitting from Rob Quiney (22 off 14), in his first appearance for the Stars this season, and a late cameo from John Hastings (8 off 2) was enough to guide the Stars home.
Brisbane were staring down the barrel early when Luke Pomersbach (1), Craig Kieswetter (13), Peter Forrest (12), Chris Lynn (10) and Hopes (2) all fell cheaply.
But Christian's heroics help them claw back into the match.
Then with Luke Wright (37 off 33) and Cameron White (17 off 13) clubbing balls to all corners, teenager Mark Steketee struck to remove the Stars captain.
Hopes then claimed the crucial wickets of dangerous Englishman Wright, Brad Hodge (1) and David Hussey (16).
And when Matthew Wade (33 off 28) was bowled by Cameron Gannon (2-35) trying to paddle him behind the wicket, the 32,696 strong crowd was in raptures.
The tension mounted as Gannon removed Marcus Stoinis for 11 in the 19th over and that pressure reached boiling point when Steketee claimed the scalp of Quiney with the Stars needing four runs from the final four balls.
But Hastings delivered at the death, smacking a six to seal the result.
Daniel Vettori (back) and Nathan Hauritz (calf) were both unavailable for the hosts.
But there could be some hope left for the Heat with Test star Ryan Harris earmarking the side's next clash with Adelaide on January 18 as his first match for the BBL season.
"It was probably the game that we needed," Hastings said.
"I think it was good that we had a really tough, hard win.
"They kept coming at us ... our boys found it tough in the middle period.
"I think it's a credit to us, we kept our heads, we kept our nerve and we got over the line."
Last year the Heat sneaked into the finals on eight competition points before winning the final against Perth and Christian hopes the Brisbane side can repeat those heroics with two matches left to play.
"We're still pretty confident because we know we're playing some pretty good cricket," he said.
"Eight points got us in last year, the only problem is that one point from the washout that the Hurricanes and the Strikers have got, that might affect us in the end.
"All we can do is try and win these next two games and hope for the best."