Chasing 147 for victory in Saturday's match at the Junction Oval, the Stars were restricted to 9-131.
All six of the Renegades' bowlers picked up a single wicket, with the Stars suffering three run-outs as well.
Bekker was playing just her second WBBL game after being called into the squad to replace injured spinner Sophie Molineux (knee).
The 20-year-old didn't let the big stage of a Melbourne derby faze her, returning the miserly figures of 1-9 from her four overs to be named player of the match.
"It's been a bit of a whirlwind," Bekker said.
When your first Big Bash wicket is MEG LANNING!— Weber Women's Big Bash League (@WBBL) How good is this for 20-year-old, Charis Bekker. #WBBL10 pic.twitter.com/sIM6B5VP13November 9, 2024
"I was at the pub a couple of days ago with my mates, and then got the call (to join the squad).
"I played against the Scorchers (earlier this week in Perth) which was really cool. And then hopped on a flight. It's been really rushed."
Bekker's maiden WBBL wicket was none other than superstar batter Meg Lanning (22 off 21 balls).
"Everyone was cheering me on, I was just trying to bowl my best ball, and it happened to be Meg Lanning, which was kind of awesome," Bekker said.
Deepti Sharma top scored for the Stars with 23, while Yastika Bhatia and Lanning were the next best with 22.
Georgia Wareham claimed the key wicket of captain Annabel Sutherland for 16.
The result improved the Renegades' record to 3-3, while the Stars are now 2-3.
Earlier, the Renegades were struggling at 5-87 before Naomi Stalenberg (26no off 17 balls) and Nicole Faltum (29 off 23) added some handy runs to lift the total to 6-146.
Marizanne Kapp (2-22) and Sutherland (2-26) led the way with the ball for the Stars.Â
🚨 Sutherland SEED 🚨— Weber Women's Big Bash League (@WBBL) That's a ripper from the @StarsBBL skipper! #WBBL10 pic.twitter.com/8kpUW72ZZUNovember 9, 2024
The Renegades were 2-54 after 10 overs when they took the Power Surge.
Although Deandra Dottin fell for seven shortly after, the Renegades cracked 29 runs off the two-over Power Surge to move to 3-83.
Alice Capsey (33 off 15 balls) and Wareham (3) fell in quick succession before Stalenberg and Faltum steadied the ship with a 55-run stand.
The Stars' run chase started at a snail place, with the scoreboard reading 1-16 after five overs.
Bhatia was lucky to still be there after being dropped by wicketkeeper Faltum in the first over when she was yet to score.
The opener scored 22 off 26 balls, but the rest of her teammates struggled for fluency as the required run rate ballooned out.