Maxwell is playing his 100th game for the Stars, the first player to reach that milestone at the team.
He won the toss, managed his bowlers superbly, claimed 1-8 from his three overs and took a crucial catch on Tuesday night at the MCG.
The Renegades could not score a boundary from the fifth to the 11th overs as they were restricted to 7-97 from their 14 overs.
Adding to the Renegades' woes, FoxSports reported batter Joe Clarke is out for the rest of the tournament with the quad injury he suffered in Friday's win over the Sixers.
They also had to leave out in-form spin bowler Mujeeb Ur Rahman because of a contract dispute with the Afghan cricket board.
It is unclear whether Mujeeb will play for the Renegades again this season.
In-form Renegades No.3 Jake Fraser-McGurk only made 14 from 19 balls before he skied a catch to Maxwell off Beau Webster's bowling.
They started brightly enough, scoring 33 from their first 2.5 overs, but once Jordan Cox was dismissed for nine they lost momentum quickly.
Quinton de Kock top scored with 23 for the Renegades against the Stars. (Morgan Hancock/AAP PHOTOS)
Fellow opener Quinton de Kock top-scored with 23 from 16 balls before Maxwell dismissed him.
Spinner Dan Lawrence claimed 2-8 from his two overs.
Cox was brought in for his first BBL game of the season and Kane Richardson returned, while the Stars dropped Corey Rocchiccioli for Jono Merlo.
Out-of-form Renegades captain Nic Maddinson remains sidelined.
The late-afternoon rain prompted a cheeky post on X from the Renegades, whose home ground is Marvel Stadium.
"Bit wet, but likely to clear. This wouldn't have happened if there was a roof, btw," they posted.
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