Chasing a miserly 65 for victory, the defending WBBL champions hit the winning runs on the first ball of the 12th over, but the win was set up earlier when their quartet of tweakers demolished a meek Thunder batting lineup.
Charis Bekker (2-14), Georgia Wareham (3-12), skipper Sophie Molineux (1-8) and Englishwoman Alice Capsey (2-12) bowled stump to stump and took wickets at regular intervals, assisted by some poor shot choices by Thunder's batters.
Molineux opened in the chase and finished unbeaten on 29 (22), finishing alongside player of the match Capsey 24 (20) as they reached 2-68.
The win sees the Gades jump into outright second on the WBBL ladder with four wins from their opening six matches, now just two points behind competition leaders, the Hobart Hurricanes.
With four regular season games to play, the Gades are in a great position to go deep into the finals again.
In the first innings the Renegades were on top right from the opening ball, restricting Thunder to 2-19 in the power play, and when in-form opener Tahlia Wilson became crafty left-arm orthodox spinner Bekker's second wicket, the home side were struggling at 3-21.
By the end of the 10th over they were in even more trouble at 5-48. England captain Heather Knight appeared their only hope of getting anywhere near triple figures, but when she fell LBW to Wareham for 20 (24), topping 100 was never on the cards.
Their 64-run total was the third-lowest in the competition's 11-season history.
Thunder star Georgia Voll, who struck consecutive boundaries before being dismissed by Milly Illingworth for 9 (7), wasn't making excuses.
"That's obviously not what we rocked up here thinking that was going to happen," Voll said on the player mic during the broadcast.
"Obviously it's pretty disappointing, to be honest.
"(The wicket) was a little bit tacky early on, but I don't think it was enough to be rolled for 65 probably, just some poor shots all around and not adapting to the conditions quick enough."
The Thunder went into the game off the back of two wins that had followed losses in their first three matches. They now sit in sixth with the job ahead of them to turn their season around and qualify for the finals.
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