Laura Harris hit the winnings runs with four balls remaining when she smashed a four between Erin Burns and Sara McGlashan.
After being set 132 for victory and needing five off the final over, Harris and Delissa Kimmince guided the underdogs over the line against the two-time reigning champions.
However Mooney was the hero, defying illness to hit a match-winning 65 off 46 balls i n front of a sold out crowd of 5,368 - and several hundred more watching from vantage points outside the suburban ground in Sydney's inner west.
After being outstanding behind the stumps during the Sixers' knock - taking two catches including a ripper to dismiss Erin Burns - Mooney was visibly struggling in the stifling heat.
The Brisbane trainers on several occasions ran out drinks to the left-hander and she was frequently down on her haunches.
But she gutsed it out, bringing up her 50 in 35 balls and putting on 84 runs alongside Kirby Short (29) for the third wicket.
There were several nervous overs after Dane Van Niekerk removed Short and Mooney in the 15th over.
Mooney was undone by a diving Ellyse Perry catch at at deep midwicket and when Jess Jonassen was caught lbw, the Heat had lost 3-5.
Yet the Heat were good enough to get over the line in what was a fitting tournament finale.
Earlier, Grace Harris (3-23) and Kimmince (2-25) fired to put the underdogs on top when they restricted the Sixers to 7-131.
In all, the Sixers hit just eight fours and three sixes during their innings and only some late hitting by Dane van Niekerk (32 not out off 15 balls) gave her side something to bowl at.
Kimmince (2-25) struck an early blow when she bowled Alyssa Healy (18) to have the Sixers rattled at 1-26 and the home side plodded along for the rest of their innings.
Harris finished with 3-23 including the key wick et of No.3 Ashleigh Gardner (23).