The home team was cruising at 95-1 when they lost three wickets for five runs, including Warner, as the visitors re-entered the game.
Tim David came to the rescue with an entertaining 42 off 20 balls, including three big sixes, to help them reach 178-7.
The hosts won the first match by three wickets, and the West Indies needed a win in their final game before the World Cup, where they face Scotland in the first round on October 17. But they only managed 147-8 in reply, with Starc taking 4-20, his best T20 figures.
They had few options to counter Warner’s 41-ball blitz, in which he hit 10 fours and three sixes.
Finch was on the teamsheet to open alongside Warner after coming in at four in the first game, but when Australia was sent into bat, it was Cameron Green who strode to the crease once more.
And, for the second time, the all-rounder was out for one. Warner sped to his 23rd T20 half-century, reaching the mark in 30 balls.
At the halfway point, they were 88-1, but the visitors pounced, with both players falling within six balls.
Finch was caught at mid-off off Obed McCoy by Rovman Powell for 15, ending an 85-run partnership, and Warner was caught and bowled by Odean Smith.
Glenn Maxwell’s poor form continued, as he was run out for one as Australia fell to 100-4, losing three wickets for five runs. However, David stabilized the ship before being lbw by McCoy.
The West Indies’ chase got off to a shaky start, with Kyle Mayers caught in the first over by Starc off his own bowling.
Brandon King (23), Pooran (2), and Johnson Charles (29) all fell in the space of 17 runs, leaving them in trouble at 76-4 after 11 overs.
To read our blog on “Mohammad Rizwan unseats Babar Azam as the top T20I player,” click here