Maxwell lifted his side off the canvas with a masterful display of power hitting, belting a game-high 90 from 52 balls at Marvel Stadium on Sunday night.
The veteran allrounder scored all 81 runs in a vital eighth-wicket partnership with tailender Usama Mir, who made a five-ball duck, and steered the Stars to 165 after they had slumped to 7-75 when sent in to bat.
Novak Djokovic was among the fans who witnessed the opening stages of Maxwell's brilliant knock, relaxing in the corporate seats ahead of his Australian Open tilt.
But the tennis superstar made an early exit and missed most of the fireworks as Maxwell plundered 10 sixes and four fours to turn the match in the Stars' favour.
Mark Steketee took 5-17 to help the Stars wrap up victory. (Matt Turner/AAP PHOTOS)
Mark Steketee (5-17) and Joel Paris (3-13) inflicted most of the damage with the ball as the Stars bowled out the Renegades for 123 in their chase.
It delivered the Stars (4-5) a fourth straight win, keeping them in the hunt for a top-four berth with one match left to play.
The Renegades (3-5) also remain an outside chance of sneaking in despite a fourth loss from their last five matches.
Tim Seifert (26 off 26) was the only batter to pass 20 for a Renegades side that managed just three sixes in 19.5 overs.
One of those was struck by Jake Fraser-McGurk (19 off 17), whose lean run with the bat continued when he was caught off Steketee.
Two of Steketee's wickets came in his first over, which also included four wides, and he finished with career-best figures.
He removed Harry Dixon and Adam Zampa with successive balls in the 17th over but was denied what would have been the season's first hat-trick .
Earlier, out-of-form Stars opener Sam Harper was trapped lbw by Tom Rogers (2-41) with the first ball of the match.
Renegades quick Fergus O'Neill (2-16) was also on a hat-trick when he dismissed Ben Duckett and Thomas Rogers but narrowly missed out when Marcus Stoinis's leading edge fell just short of Kane Richardson at mid-off.
Richardson (2-40) was the man to eventually dismiss Maxwell, who chopped onto his stumps in the final over, but the Renegades quick limped off a few deliveries later with hamstring tightness.
Dixon marked his Renegades debut with a superb piece of fielding to run out Paris.
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