Opting to bat, Australia scored a competitive 178 for eight in 20 overs, riding on Glenn Maxwell's 45 and Brad Hodge's 35. West Indies got the runs with a couple of balls to spare.
Needing 31 off the last two, Sammy (34 no, 13 balls) smashed Mitchell Starc for 19 runs in the penultimate over to bring the equation down to 12 in the final over bowled by James Faulkner. The skipper hit two fours and three sixes.
After two dot balls, Faulkner bowled a full-toss that Sammy hit over long-off for a six to bring the equation down to six from three balls. Sammy then hit the next straight over the bowler's head and threw his bat running towards the dug-out as his delirious mates joined in the celebration.
Sammy had said yesterday that he doesn't care whether "James Faulkner likes West Indians or not" but he gave a fitting reply to the bowler as Gayle again did the Gangnam jig with vengeance as poor Faulkner could only look on.
The win brightened West Indies' chances for a semi-final berth while Australia will find it difficult to make a comeback in the tournament.
After a couple of relatively quiet matches, Gayle picked up the Australian attack for some special treatment. He set the tone from the third delivery of the second over bowled by left-arm speedster Mitchell Starc. Starc pitched it up outside the off-stump and was smashed through covers with bare minimum footwork.
The next was a fuller delivery on the middle and was hit over the bowler's head that just dropped in front of the ropes. The next two back-of-the-length deliveries were pulled through mid-wicket and square leg region.
In the next over from Doug Bollinger, Gayle got his first six of the game with a pull over square leg fence. His second six was a flat-batted hit over long-on off Shane Watson.
With Gayle picking up the tempo, it became easier for Smith at the other end, and he did his bit with an uppishly driven four off Starc that brought up the team 50 in 4.2 overs.