Set 267 to win after Bailey's unbeaten 125 rescued the Australian innings, the West Indies were cruising at 159 for three in the run chase, before the return of Starc to the attack turned the match again as the tourists were bowled out 212 in the 39th over.
Starc (5-32) had claimed the first three wickets in the West Indian innings, all lbw, to have them reeling at 33 for three, but when he came back into the attack the Australians were struggling, with opener Kieran Powell and Dwayne Bravo putting on a century partnership for the fourth wicket.
However, the left-armer, who took 5-20 as the Australians routed the West Indies for 70 in Friday's opening game en route to a nine-wicket victory, struck two telling blows.
After spinner Glenn Maxwell ended the Powell and Bravo partnership at 126 runs by having the latter caught behind for 45, Starc removed Powell, adjudged lbw for 83 on a decision review and Devon Thomas (0) in successive balls to claim his second five-wicket haul in as many matches. Thomas was given out in quite bizarre circumstances, with umpire Nigel Llong giving the batsman not out on a caught behind appeal, but third umpire Asad Rauf reversing the decision despite the apparent lack of any evidence at all to suggest the West Indian hit the ball.
When Darren Sammy fell for eight a short time later, the West Indies had lost 5-20 and slumped to 179 for eight.
Sunil Narine (24) briefly lifted West Indian hopes when he belted four sixes in a row off Maxwell (4-63), before being stumped from the last ball of the same over.
Earlier, brilliant catching by the West Indies had Australia in deep trouble at 98 for six, before Bailey steered a spirited fightback that saw the home team make 266 for seven from their 50 overs.
Bailey reached his century by blasting Kemar Roach over mid-wicket for six in the 49th over. He then finished the innings in style, hitting three sixes in the final over from Bravo as the Australians plundered 25 runs.
Bailey hit 30 runs from the last six balls he faced in the innings, facing 110 deliveries overall and hitting 10 fours and one six. – Sapa-AFP