After Katie Mack's 50 and Laura Wolvaardt's 46 carried the Adelaide team to 8-153, an impressive bowling display led by Darcie Brown (1-17) and Amanda-Jade Wellington (2-19) restricted the reigning champions to 8-135.
The chase started brightly as Heat openers Georgia Redmayne and Maddy Green put on 79 for the first wicket, the former bringing up her first fifty for the Heat, and the fifth half-century of her WBBL career, from 37 deliveries.
Green was unlucky to be run out on 25, diving when her bat bounced despite being over the line, and a searing yorker from 17-year-old quick Brown had Heat skipper Jess Jonassen bowled for three.
The momentum swung when Sarah Coyte claimed the key wicket of Redmayne on 65 from 47 balls, while a double-strike from leg-spinner Amanda-Jade Wellington removed Laura Kimmince (8) and Amelia Kerr (3), the latter falling to a double-act that saw the ball ricochet off the hands of Madeline Penna, and a diving Tahlia McGrath hang on to a brilliant catch.
Pressure mounting, the wickets continued to tumble, as Grace Harris holed out for 10 and Nadine de Klerk (6) was run out thanks to a brilliant throw from Brown in the deep.
A collapse of 5-10 stifled the run rate, before Coyte struck two final-over Sixes to lift the Adelaide side to 8-153.