After being dropped twice by Brendan Doggett, James Vince smashed a match-winning 75 off 46 balls on Sunday night as the home side posted 7-177, a total which proved far too big for the Heat.
The Sixers broke a two-game losing streak, and jumped into second place on net run rate, as the Heat were bowled out for 98 in the 19th over in front of a crowd of 14,921.
The run chase was as good as over after Max Bryant (0) and Chris Lynn (2) fell cheaply to have the Heat reeling at 2-16 in the fifth over.
The dismissal of Lynn, who skied Sean Abbott to Jack Edwards, would have had Heat fans looking for ways to cut power to the SCG light towers - after an electricity grid failure saved their blushes in the recent clash with the Sydney Thunder.
Highly-touted red-headed spinner Lloyd Pope - recalled after a couple of nervous showings in his two maiden BBL games - underlined his talent when he lured Jimmy Peirson out of his crease to have him stumped.
The 19-year-old also collected the prized scalp of Brendan McCullum (27 off 31) to finish with 2-19.
Sean Abbott (3-18) and Tom Curran (3-16) were also instrumental in the rout.
Earlier, the Sixers looked headed for a mediocre total before Vince and Jordan Silk hit the accelerator midway through their innings.
After being 3-89 at the 12-over mark, they put on 67 over the next five overs, before Vince was caught at third man by Lynn off Mujeeb Ur Rahman.
Vince was dropped on 31 after Doggett failed to get under a towering shot which hung in the air for six seconds.
He was given a third life by Doggett on 57 when he was dropped at deep mid-wicket in the 15th over.
Silk came undone when he was bowled by Josh Lalor, who was the lone shining light for the Heat after taking his best BBL figures of 5-26