The Renegades batted first and Aaron Finch (84 not out) and Tom Cooper (60) ensured they set a competitive total of 5-163 after a horror start with three wickets in one Jackson Bird over, but wickets were always going to be the key defending their total.
And the Renegades managed only one wicket in the Stars innings, Luke Wright for 17, as White (84 not out) and Maxwell (58 not out) saw the Stars comfortably home reaching 1-167 off 16.2 overs with nine wickets and 22 balls in hand.
The result means that the Stars remain unbeaten after four matches while the Renegades' two-match winning run emphatically came to an end and they now have just those two victories from five games in the BBL of this summer.
The second Melbourne derby of the BBL took place at Etihad Stadium and drew a terrific crowd of 42,837, and they saw the Renegades bat first but make a horror start.
Bird was the destroyer for the Stars claiming the wickets of Michael Hill (8), Jos Buttler (0) and Ben Rohrer (0) in the second over of the match, and he was then on a hat-trick and went up for a big LBW shout but the ball to Cooper was going over the stumps.
It was a slow build from there for both Finch and Cooper, but at least they stopped the flow of wickets for the Renegades and once settled, the big shots started to fly.
Cooper was the first to get going for the Renegades as he past 50 and ended up making 60 from 44 balls with four boundaries and two sixes when caught by White off the bowling of John Hastings with the score 4-119 in the 17th over to end a terrific 102-run partnership with Finch.
Finch then got no support from Peter Nevill (3) and Matthew Gale (0 not out), but he didn’t need much help in the final overs as he put on an incredible display of power hitting.
Finch brought up his 50 with a six off John Hastings on the last ball of the 17th over, and then took Faulkner for one to start the 19th when it was awarded the maximum after hitting the Etihad Stadium roof.
It was then in the last over that Finch took the Renegades to a decent score when he smashed Victorian teammate Clint McKay with three sixes and a four with 25 runs off the over as his side finished on 5-163 from the 20 overs.
Bird finished with 3-24 from four overs with Lasith Malinga taking 1-21 from four, Hastings 1-35 from four, Faulkner 0-28 from four and McKay 0-50 from four.
James Pattinson started well with the ball for the Renegades going for just two runs from the opening over but the Stars made up for that in the second over smashing 15 off Gale.
The Renegades' fielding also let them down with Jos Buttler dropping a sitter off Rimmington with White on 30 and Muttiah Muralitharan also missed a catch off his own bowling with Wright on just 13 as the Stars got off to a solid start.
English all-rounder Wright made just 17 from 21 balls before being caught in the deep by Michael Hill off Aaron O'Brien, but that was to be the last joy of the night for the Renegades as White and Maxwell came to the crease together.
The pair ended up combining for an unbeaten 98-run partnership from just 50 balls at a run-rate of almost 12 an over as the Stars cruised to victory with almost four overs to spare.
The match was taken out of the hands of the Renegades once and for all in the 13th over when Maxwell smashed four sixes off left-arm spinner O'Brien.
By the end of that 26-run over, the Stars were 1-124 and then Maxwell took three more sixes off one over from Pattinson as the tournament favourites cruised to victory.
White finished not out on 84 from 49 balls with six fours and four sixes for the Stars with Maxwell joining him not out on 58 from 28 deliveries with two fours and six sixes.
Muralitharan was the pick of the Renegades' bowlers with 0-30 from four overs with Nathan Rimmington finishing with 0-19 from two, Pattinson 0-37 from 3.2, Gale 0-41 from four and O'Brien 1-38 from three.