Blue-chip pacemen Sean Abbott and Ben Dwarshuis, along with in-form spinner and player of the match Joel Davies, each took two wickets to restrict the Heat to a paltry 9-114.
It should have been a cakewalk for the Sixers but the Heat have shown this season that they are never beaten.
Brisbane had the Sixers 7-56 in the 11th over and at that point appeared on track to break the record set by Perth Scorchers in 2013-14 against Melbourne Renegades, when they defended 7-117. That total remains the lowest to have been successfully defended in the BBL.
Davies (35no) and Hayden Kerr (26no) then combined for a composed and crucial unbroken 62-run stand in 49 deliveries for the eighth wicket.
The run chase was chaotic and thrilling before Kerr hit a massive six to win it with eight balls to spare.
Brisbane's 20-year-old rookie Oli Patterson picked up Babar Azam (two) and Josh Philippe (0) in consecutive deliveries in his first over.
The Sixers were well contained by the Heat bowlers and slumped to 5-47 in the ninth over when Matt Kuhnemann dismissed Jordan Silk (six) and Jack Edwards (0) in consecutive deliveries.
Skipper Moses Henriques (26) slapped Jack Wildermuth to Kuhnemann and it got worse for Sydney when Matt Renshaw caught and bowled Ben Manenti (two) to make it 7-56.
The 22-year-old Davies, who was magnificent with ball and bat, and Kerr then took control to saves Sixers' blushes.
"I'm pumped," Davies said. "One of my goals for the year was to have a man of the match performance and it was good to have it in such challenging conditions."
The Sixers and Heat are both on six points but the Sydney outfit have played one less match and have a far better net run rate.
Brisbane have won all three of their home matches but are winless in their four away games and continued the win-loss sequence that has been the story of their summer.
The Heat made the bold call to leave out experienced overseas signing Colin Munro and open with Lachlan Hearne but he made just one.
Wildermuth (31 off 17) went big in the powerplay with one of his two sixes launched 84m and out of the venue before he was cleaned up by Abbott.
Max Bryant (three) was unable to replicate his player of the match heroics of Saturday night.
Sixers left-armer Dwarshuis removed Bryant and skipper Nathan McSweeney (11) in the same over as the Heat slumped to 4-50 in the eighth over.
Abbott, playing his 200th T20 match in all competitions, was on song as he extended his margin as the BBL's all-time leading wicket taker.
Dwarshuis, considered unlucky to miss out on Australia's T20 World Cup squad, was superb.
The unbeaten last wicket stand of 23 by the Heat's Patterson and Tom Balkin was their side's second-best, highlighting their batting woes.
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