Gayle smashed six sixes and six boundaries for 88 off 50 balls and Fletcher hit 53 off 32 deliveries, including seven boundaries, as West Indies reached 172-3 to eclipse Australia's total of 169-7 with 25 balls to spare at The Oval.
The pair's stand was the third highest international Twenty20 partnership. Fast bowler Brett Lee received most of the punishment, with figures of 0-51 from three overs at one stage.
Gayle collected 27 runs off Lee's third over after hitting three massive sixes, one of which went out of the ground and into an adjoining school and another that landed on the roof of a stand bordering long on.
Australia needs to beat Sri Lanka at Trent Bridge to have any chance of advancing to the Super 8 stage from Group C. West Indies next plays Sri Lanka on Wednesday at Trent Bridge. David Warner, who has played only one first-class match, had earlier led Australia to a defendable total after his team had lost Shane Watson and Ricky Ponting in consecutive balls of the first over to be 3-2.
Warner hit 63 off 53 deliveries, including six boundaries and a six. Jerome Taylor had Watson caught by Ramnaresh Sarwan and then trapped Ponting lbw after Australia had won the toss and elected to bat.
Three overs and 12 runs later, Michael Clarke was caught for 2 by Suliemann Benn off Fidel Edwards to leave Australia reeling. However, Warner and Brad Haddin added 66 in eight overs before the latter was caught by Benn off Kieron Pollard for 24. Warner was out in the 16th over with the total on 113, becoming Benn's third catch of the innings to give Dwayne Bravo a wicket.
The Hussey brothers put on 30 in 14 balls before David was caught by Fletcher off Bravo. Mitchell Johnson was the last man out, caught by Bravo off Edwards for 9, leaving Michael Hussey not out on 28 from 15 balls. Bravo had figures of 2-31, while Taylor took 2-33 and Edwards 2-34.
West Indies' reply was immediate and murderous in its intent. After Lee had been clobbered for 27 off the fifth over of the innings, West Indies was 71-0 and the pair soon brought up their 100-stand in 51 balls.
Fletcher was out after skying a ball from Johnson to be caught by David Hussey in the 12th over. Gayle followed 18 balls later, caught by Watson off Lee to leave West Indies on 157-2. Next over, Xavier Marshall was caught by Hopes to give Johnson a second wicket.
But Sarwan (8 not out) and Shivnarine Chanderpaul took West Indies to victory.
