With the tourists chasing 161 for victory, a brilliant run-out by Dwayne Bravo to dismiss David Warner sparked the home team into action as Australia ended on 9-146 in reply.
The result ensures the two-match series finishes 1-1 and means Australia's seven-year wait for a T20 series win overseas continues.
Warner, on the end of constant chatter by the West Indies fielders after giving Kieron Pollard a send-off during the Windies' innings, scored 58 off 43 balls and appeared to have Australia in control in their chase.
But his innings was ended in dramatic fashion by Bravo, who threw down the stumps at the striker's end from mid-on to catch Warner short, stalling Australia's innings and enabling the Windies to snatch the victory.
Fast-bowler Fidel Edwards finished with 3-23 off his four overs as did Marlon Samuels, while Bravo took two wickets in the final over to finish with 2-27.
Earlier, opener Dwayne Smith belted his maiden T20 international half-century as the Windies made 160 batting first.
Smith scored 63 off just 35 deliveries, including six fours and four sixes, to lift the Windies to 2-100 inside 10 overs.
But the former NSW representative's demise sparked a collapse as the Windies lost their last eight wickets for 50 runs.
Johnson Charles (37), who shared a 72-run opening stand with Smith, and Dwayne Bravo (23) were the only other Windies batsman to reach double figures.
Brett Lee took 3-23 to lead Australia's bowling effort while Clint McKay (2-24) and Shane Watson (2-26) supported with two wickets each.
Youngster James Pattinson had a day to forget, conceding 0-34 off his two overs including three sixes to Smith in one over.
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