The Heat were cruising at 1-104 after 12 overs in Saturday's clash when they called for the Power Surge.
Scorchers paceman Jason Behrendorff snared the scalps of Sam Heazlett (34 off 30 balls) and Jimmy Peirson (three) in an inspired over to help turn the momentum, with the Heat managing just eight runs from the two-over Surge.
But just as the home side looked set to turn the screws, Bryant came to the rescue with a quick-fire 31 off 14 balls.
Bryant, who used to open alongside Chris Lynn before falling out of favour and being demoted down the order, cracked two fours and three sixes to give his side a vital push.
Behrendorff was the pick of the bowlers with figures of 2-26 from his four overs.
His figures would have been much better if it wasn't for three thick edges from opener Josh Brown (25 off 12 balls) in the first over of the match that all went to the boundary.
Matt Kelly, who pipped spinner Peter Hatzoglou for a spot in the XI, finished with 2-37 after snaring two late wickets.
The mercury was still hovering around 38 degrees when the match began at 4.30pm WST.
Behrendorff removed Heazlett and Peirson with rising deliveries that were hooked to fine leg in the 13th over, and Cameron Bancroft took a good catch low to the ground while looking into the sun to send Nathan McSweeney packing for 41 off 37 balls.
A six off the final ball of the innings by Xavier Bartlett ensured the Heat surpassed the 170 mark, with the Scorchers now facing a tricky run chase.Â
Perth are aiming to snare their fifth BBL title.
The Heat, who won their one and only title 10 years ago, have the chance to pull off a remarkable rags-to-riches tale.
Brisbane were sitting last on the ladder in mid-January, but they won four of their next five games to scrape into the finals in fifth spot.
The Heat have been a dominant force during the finals, defeating the Sydney Thunder, Melbourne Renegades, and Sydney Sixers all on enemy territory to secure a spot in the decider.
But they were given short shrift in the local newspaper in Western Australia, with the team labelled "nobodies" due to their lack of star power after losing Usman Khawaja, Matt Renshaw, Mitchell Swepson and Marnus Labuschagne to Test duties.
"Just FYI. We keep our receipts," the Heat tweeted on Saturday alongside a picture of the liftout that was headlined: "Scorchers versus a bunch of nobodies".
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