The hosts posted 8-172 before Inglis (78 not out from 33 balls) and Cameron Green (56no from 32) led Australia to 2-173, and victory with 28 balls to spare.
The pair put on a unbroken 131-run partnership off just 64 balls as Australia took a two-nil lead in the five-match series.
Inglis was brutal with the bat, blasting a half-century from just 22 deliveries - hitting five sixes and seven fours all-up.
And an equally aggressive Green cracked four sixes and three fours after starring a three-wicket win in game one with 51 from 26 balls.
Australia sent Glenn Maxwell out to open in the innings after dropping Jake Fraser-McGurk but he made just 12 from 10 balls.
Captain Mitch Marsh's 21 from 17 included two sixes but when he fell, the match was in the balance at 2-42 in the sixth over.
Inglis and Green then launched an audacious attack on the West Indian bowlers, making light work of the run chase ahead of the next three games in St Kitts on Saturday, Sunday and Tuesday (all AEST).
With Inglis in full flight, Green posted his half-century from 28 deliveries.
Earlier, Australia's spinners were vital in restricting the West Indies batsmen.
Legspinner Adam Zampa claimed 3-29 from four overs and offspinner Glenn Maxwell 2-15 from two as they put the brakes on the hosts after a brisk start.
Opener Brandon King (51 from 36 balls) embarked on an early blitz, reaching a half-century from 33 balls.
West Indies were 0-59 after seven overs but Zampa struck with the last ball of his first over, the eighth of the innings, when King skied to cover.
On the next ball - the first of Maxwell's spell - Shai Hope (9 from 13) departed when skipper Marsh took a fine catch running with the flight of the ball at mid-off.
West Indies were 2-73 at the midpoint but lost Shimron Hetmyer (14 from 10) in the next over when caught on the square leg boundary to give Maxwell another wicket.
Zampa struck twice in the 14th over, dismissing Roston Chase (16 from 16) and Sherfane Rutherford (0 from 2), leaving the hosts wobbling at 5-98.
Hometown hero Andre Russell, in his last international match, then produced some farewell fireworks by cracking 36 from 15 balls featuring four sixes and two fours.
Australia made two changes from the team that won the series-opener by three wickets.
Left-arm spinner Matt Kuhnemann was summoned for his T20I debut, replacing paceman Sean Abbott, while batsman Jake Fraser-McGurk was dropped with middle-order blaster Tim David returning from a hamstring injury.
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