Match Tied (Royal Challengers Bangalore win one-over eliminator)
Fresh from a match-winning 59 not out in the previous game, Maxwell stepped up to lead his team to another win over their derby rivals.
He stitched a superb 115-run stand with the in-form Nick Larkin to mow down the imposing 169-run target with eight balls to spare.
The Stars had a troubled start to their chase as they lost Marcus Stoinis for a duck on the third delivery of the innings.
Stoinis, who currently sits atop the list of leading run-getters in this year's edition of the BBL, miscued a slog off the bowling of Samit Patel that was pouched by the man at mid-off.
Hilton Cartwright's dismissal further derailed the Stars' progress as they were reeling at 54-3 by the end of the seventh over.
Amidst the climbing asking rate, Maxwell and Larkin steadied the team by piercing the gaps with nifty strokeplay.
The Stars skipper then launched into a six-hitting frenzy in the latter half of the chase with some sumptuous hits from his bat travelling the distance deep into the stands.
Maxwell used the crease well to dispatch even the good-length deliveries to the boundary fence.
His innovative technique enabled him to put on a clinical display as he finished off the match in style with a terrific tonk over square leg off his Renegades counterpart Dan Christian.
The 31-year-old Aussie slammed seven maximums in his belligerent 45-ball 83 while Larkin provided solid support with a 28-ball 33.
Earlier in the game, the Stars' bowlers delivered a splendid death overs performance after Shaun Marsh's sublime knock threatened to pile on their misery.
Marsh's opening partnership with Marcus Harris lasted 63 balls as they racked up 86 runs but the middle order failed to capitalise on the momentum in the face of disciplined bowling from the Stars.
Haris Rauf was the most economical of the lot, giving away just 25 runs in his four-over spell and grabbing a wicket whereas fellow pacer Nathan Coulter-Nile claimed two scalps to restrict the Renegades to 168-7.