Held to a below-par 6-163 and with the Heat cruising at 1-67, the reigning champions looked destined to slump to a third loss in four games.
But pinpoint bowling from Lance Morris (3-26) and AJ Tye (4-14) turned the game on its head and fired the Scorchers to a comfortable 35-run win.
It avenges their loss to the Heat just three days ago and moves them into second on the table, keeping them in with a chance of a home final.
They face the third-placed Sydney Sixers on Tuesday night with the winner to seal second, and keep a chance of hosting the grand final should they win their opening playoff contest.
Sitting pretty at 1-67, the Heat lost 3-17 off 26 balls to allow the Scorchers back into the game.
Brisbane's Nathan McSweeney (three) was caught behind off Tye before a stunning leg-side take from keeper Josh Inglis to dismiss Matthew Renshaw (one) heaped the pressure on at 3-82.
Two runs later, Jimmy Peirson (42) chipped Ashton Agar to point to cap the turnaround.
Max Bryant (29 off 17 balls) slogged some late runs but it was far too little for the Heat.
Tye cleaned up the tail with three wickets in the game's last five balls to secure victory.
Aaron Hardie (1-22) and Jason Behrendorff (1-23) were also important in tightening the screw for Perth.
The Scorchers' Laurie Evans heaped praise on the bowlers' fightback.
"(The bowling) just flipped the game our way ... we've always prided ourselves on having good power-surges whether with the bat or the ball," he told Fox Cricket.
"It's a lot easier to hit the ball here, rather than bat properly ... I find hitting sixes a lot easier … today I tried to bat normally and I couldn't get going.
"We've got a great rivalry against the Sixers, the two best teams in the history of this competition over the years, so it'll be nice to welcome them over here."
Alongside his side's bowling brilliance, Perth No.7 Nick Hobson played a key role in the win, crunching an unbeaten 48 off 30 balls to help his side post a respectable total.
Star duo Hardie (nine) and Inglis (five) failed as the Scorchers slumped to 4-49, but Cooper Connolly (35) and Evans (26) aided the recovery before Hobson's late rally.
Heat bowler Michael Neser took 2-21, along with an outrageous diving catch while chasing the ball over his head, to get rid of Connolly.
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