Keiron Pollard produced an innings of 109 not out to help West Indies post a target of 221 for Australia in Sydney.
The tourists were 45-5 early on in their innings before Pollard struck 11 fours and two sixes to give his side a slim chance of securing their first victory of the series.
Despite winning the toss, West Indies struggled to get going and they were soon up against it as Mitchell Johnson ripped through their top order to leave them on 17-3.
Ben Cutting soon got in on the act to pick up three wickets in quick succession as West Indies lost seven wickets before entering three figures.
Pollard was providing some firm resistance for the Caribbean side and he recorded his 50 to move his team past 150.
It was evident that he was taking responsibility of his side's innings as the lower-order batsmen entered the fray and after two huge sixes down the ground, Pollard finally registered his third one-day international century off the penultimate over of the innings.
