In the first game of the 10th edition of the WBBL, the Heat suffered some nervous moments in the chase at the Adelaide Oval before reaching the Strikers' 5-133 with 12 balls to spare.
Charli Knott (44 not out) proved a steady hand for Brisbane when they lost 3-9 as they closed in on the target.
Australian star Megan Schutt claimed two quick wickets to give Adelaide a sniff of a miracle victory.
But Knott, 21, closed out the win with a lofted drive for two runs to be named player of the match.
Adelaide, who are gunning for a third-straight title, never got going with the bat on their home ground despite an unbeaten 51 from captain Tahlia McGrath.
In her first game for the Heat, Indian quick Shikha Pandey took 2-14 from her four overs, including the key wicket of Strikers opener Laura Wolvaardt.
The match was the first of three games to take place on the opening day of the tournament on Sunday.
In a double-header at the Adelaide Oval, the Melbourne Renegades will later battle the Sydney Sixers.
To finish off the day, Perth will host the Melbourne Stars at the WACA Ground.
Wins assume extra significance this year after the tournament was reduced from 14 games to 10.
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