The Stars defeated Brisbane Heat by five wickets at the Gabba in a breakthrough win after losing their opening five games this season and the final three of last year's campaign.
The Heat made 7-149 batting first thanks to a blistering and unbeaten 77 off 48 deliveries by Max Bryant, during which Maxwell took one of the greatest catches seen in the BBL in an all-round brilliant individual fielding exhibition.
Brisbane Heat bowler Xavier Bartlett (c) took 4-10 in a losing effort against the Melbourne Stars. (Dave Hunt/AAP PHOTOS)
The hosts had the perfect start to the Stars' run chase with pacemen Xavier Bartlett (4-10) and Spencer Johnson rocking the top order to have the visitors teetering at 3-14.
The Stars needed someone to stand up and Stoinis (62 off 48) and England import Dan Lawrence (64no off 38) delivered in a 134-run partnership for the third wicket.
Stoinis walloped Paul Walter for four boundaries in one over and paced the run chase perfectly, bludgeoning anything loose to secure his first win this season as Stars captain. Lawrence upped the ante at the end to take the pressure off Stoinis in an innings of class.
Maxwell has done a plethora of freakish acts of genius in T20 cricket but he took it to the next level with a classic catch for the ages, his fourth for the innings.
The veteran leapt metres over the long on boundary to catch the ball in one hand before throwing it back into the field of play while in the air. He calmly stepped back over the boundary rope to complete the catch and send a stunned Will Prestwidge (4) on his way.
The ball seamed around from the start and justified the decision by Stoinis to send the Heat in.
Heat skipper Colin Munro (1) continued his dire form in the BBL this summer and now has 23 runs in four innings.
Fellow opener Tom Banton (13) was the second wicket early for Mark Steketee against his former franchise.
When veteran Peter Siddle clean bowled Nathan McSweeney (9) with the first ball of his spell the hosts were on the rack.
Walter (21) threatened to cut loose before Bryant took charge, carting Steketee for three sixes and thrice lofting Siddle into the crowd twice with massive blows. He finished with six maximums in a blistering knock that included brute power and deft ramp shots to give his bowlers a total to defend.
Stoinis and Lawrence stepped up in the run chase to consign defending champions Heat to their third consecutive loss.
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