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The much-hyped Stars fell to 0-3 for the season as Brisbane cruised to victory at the MCG, reaching their target of 142 with five overs to spare.
Promoted to open the batting, master-blaster Chris Lynn plundered three sixes on his way to 63 off 46 balls.
His 101-run stand with Heat captain Brendon McCullum was the pair's third BBL hundred-partnership.
The Stars would have had Lynn out for a third-ball duck if not for captain John Hastings dropping a sitter at mid-off in the first over.
It was a welcome return to form for Lynn, who underwent shoulder surgery in July and is the third-highest run scorer in BBL history.
McCullum faced just 27 balls before bringing up his fifty with a six off Liam Bowe.
He departed three balls later, caught by Rob Quiney at long off for 61.
Glenn Maxwell earlier fought a lone hand for the Stars with a composed 50 off 39 balls, although the frustrated allrounder was unable to find many positives after the game.
"We're not looking like going anywhere but bottom at the moment," he said.
"We're playing terrible cricket. We're not probably playing together as a team ... we were putrid today."
Swepson earlier took 3-14 off four overs, including the key scalp of Kevin Pietersen, after the Heat won the toss and elected to bowl.
The impressive legspinner frustrated the Stars' batsmen with his variations of pace, tempting Luke Wright (19) into a wild attempted slog which had him easily stumped.
Pietersen (30) looked in solid touch on return from a one-game break before being caught at long on off a well-flighted Swepson delivery.
"It was a nice wicket to bowl on out there tonight. I think it was pretty conducive for the spinners," Swepson said.
"[The Stars] are just going through a bit of a rough patch at the moment ... they'll bounce back and find a way."
Swepson, whose domestic form has earned praise from spin great Shane Warne, also impressed Ricky Ponting, who has been linked to coaching Australia's Twenty20 side.
"Really good bowling from Swepson," Ponting said on the Ten Network.
"A lot of thought has gone into the way he's approached it."
Pakistan legspinner Yasir Shah took 1-16 off four overs and was unlucky to have an lbw appeal against Quiney turned down.