Chasing 152 for victory after the visitors batted first and hit 7-151, the Heat looked to be in serious trouble when they slumped to 3-22 in the fifth over with Nathan Coulter-Nile (3-37 off 3.4 overs) dismissing Luke Pomersbach (four) and Joe Burns (eight) in the space of 13 balls.
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But that collapse was Lynn's cue to enter the fray and he did so in a big way as he smashed 81 off just 53 balls, including four boundaries and six sixes, to singlehandedly drag the hosts to 7-152 and a thrilling victory.
Veteran spinner Brad Hogg was also a menace for Perth with the ball as he ended up with 3-21 from his four overs.
Earlier in the evening, Mitch Marsh (57 not out off 35) was pivotal in ensuring the Scorchers amassed a competitive total after they were looking shaky at 6-94 in the 15th over.
Marsh top-scored for Perth, and whacked five fours and a huge six in his entertaining knock, while his brother Shaun Marsh also compiled a useful innings of 37.
Ben Cutting (3-31 off four) was the pick of the Brisbane bowlers and he was ably assisted by Alister McDermott who claimed 3-38 from four, including the wickets of top-order batsmen Simon Katich (10) and Sam Whiteman (six).