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West Indies were 205 for nine after being sent to bat first after the visitors won the toss, but took five wickets after the midpoint to keep the pressure on Australia chasing 206 to win.
The visitors went on to clinch the win with four balls to spare and took a 4-0 lead in the series courtesy of Cameron Green's knock of 55 off 35 balls - his third half-century in the four matches.
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