Adelaide posted its second-largest total of the season with 8/176 off the back of contributions throughout the order, but didn’t have a batsman cash-in with a match-winning score.
Jon Wells (30 from 27 balls), Colin Ingram (28 from 21) and Alex Carey (24 from 24) all made promising starts without punishing the Heat.
Brisbane then slumped to 3/18 in reply in the third over.
That was before Player of the Match Matthew Renshaw strode to the crease and crushed an unbeaten 90 off only 50 balls to flip the match on its head.
With support from Brendon McCullum (51 from 39 balls), Renshaw struck his maiden Big Bash half-century to deliver a crushing blow to the Strikers’ finals hopes.
The Heat reached the target total with eight balls to spare.
The returning Peter Siddle was the Strikers’ best with the ball, taking two early scalps and finishing with figures of 2/39.
Young allrounder Cameron Valente had Chris Lynn caught behind for a duck while Rashid Khan (1/30) was Adelaide’s only other wicket-taker.
Adelaide will complete its BBL|08 campaign at Adelaide Oval on Saturday against the Perth Scorchers with both clubs vying for the Jason Gillespie Trophy.