Maitlan Brown (21no off 15) and Mathilda Carmichael (28no off 20) got the Sixers home with one delivery remaining in a brilliant run chase at Allan Border Field that had an unusual twist.
Heat spinner Amelia Kerr fielded a throw with a towel in her hand that she had been using to dry the ball, an illegal act which incurred a five-run penalty that ultimately proved costly.
Earlier on Tuesday, the Adelaide Strikers had taken the outright lead on the WBBL ladder after a rescue mission by opener Laura Wolvaardt set up a thrilling three-run win over Sydney Thunder.
The clash in Brisbane had ramifications for the finals with Sixers moving to fifth on 12 points, two behind Brisbane who are in fourth and not yet across the line for a finals berth.
The Sixers still have significant ground to make up on the Heat in their net run rate with each side to play Sydney Thunder in their final match.Â
Kerr (64 off 44) and Mignon du Preez (42 off 27) had combined for their third half-century stand of the season to take the Heat to 7-176, with an unbeaten Charlie Knott cameo of 29 from 10 deliveries the icing on the cake.
The Sixers were given a fast start by Ellyse Perry (20) after the star allrounder had taken three wickets with the ball.
Erin Burns (35) walloped three sixes in her best knock of the summer and Ash Gardner (36) chipped in before Brown and Carmichael provided the late fireworks.
Earlier at Cricket Central it was Wolvaardt's class and composure in an unbeaten 70 proved the difference after Adelaide were sent in.
She grafted as wickets tumbled at the other end before unleashing at the death. The South African star combined with Megan Schutt (16no) to take 38 runs off the final three overs and lift the defending champions to 7-121.
The Strikers' bowlers were brilliant early with Jemma Barsby dismissing dangerous Chamari Athapaththu (0) in the first over and Schutt snaring Phoebe Litchfield (one) in a deep cover trap in the second.
The hosts were meandering along at 5-53 after 14 overs until Tahlia Wilson (33 off 23) and Sammy-Jo Johnson (26no off 14) threatened to get their side home.
A crafty last over by spinner Anesu Mushangwe (2-24), where she conceded just five runs, clinched the win and kept the Thunder to 7-118.
Australian pace bowler Darcie Brown (1-15) returned from a hamstring injury for her first WBBL game of the season and found instant form.
The Strikers went to 18 points with the win, two clear of Perth Scorchers and three ahead of Thunder.
Thunder looked good early.
Marizanne Kapp's opening over of the innings was made to order. The first ball of the innings was straight and Katie Mack missed to be plumb lbw. The South Africa international snuck the fifth delivery under the bat of Australia star Tahlia McGrath (four) to have the visitors 2-4.
The low bounce was utilised perfectly by the Thunder attack as they put in an accomplished display of stump-to-stump bowling at its best.
The Strikers were 4-47 after 10 overs but Wolvaardt then stepped up to play the only substantial innings of the match.
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