After being dropped twice by Brendan Doggett, 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 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.
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.
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.
Without his efforts, things could have been really ugly for the Heat.