Australia extended their lead in the series on Friday to 4-0, when they snatched a dramatic one-run victory in the fourth ODI at Warner Park, much to the horror of a strongly partisan, near capacity, holiday crowd.
Shane Watson kept his nerve in the final over, as the seventh-wicket pair of Denesh Ramdin and Darren Sammy failed to carry West Indies over the threshold.
Australia had set West Indies 283 for victory from 50 overs, and successfully defended the target score, when Watson - with the home team needing eight runs from the last over - conceded six runs from the final six balls.
"A victory on Sunday and a 5-0 series sweep will mean a lot to us, since it has been our goal when we arrived in the Caribbean to win every match we play on this tour," Australia captain Michael Clarke told reporters.
"It would be important to us because the new guys coming into the side would get to be a part of a winning side, and we would get to show them the level of performance we expect from them.
"This series is not over for us just yet. We want to win every match, and the fourth ODI was a good example of this, so we will be out there on Sunday looking to win, and giving our best."
For West Indies, Friday's result was another setback on their road to recovery, after Ramdin and Sammy choked under the pressure, and their coach John Dyson admitted it was hugely disappointing.
"We are still playing to avoid being beaten 5-0, and the message to the team is that we still have one match to play," Dyson said.
"It would be great to win one match in this series. Australia have said from the start that they wanted to win 5-0, but we do not want to lose 5-0.
"From my point of view, it's much better losing by one run than losing by 100 runs. The fourth ODI could have been decided with one hit. A big hit in the last over, and the game would have been over.
"But I'm never happy that we lose matches. Whether we should have won it or not is a matter of conjecture. Australia got 282 on the board, and that's a reasonable total, and if you look at the run chases we had in this series, we have not made 282 or come close to getting lesser totals than this.
"We were always going to have to bat well, and I think we batted pretty well, but it came down to a one-hit game in the last over, and we just couldn't quite do it."
South Africa and Pakistan are the only sides that have achieved ODI series sweeps in the Caribbean.
They both accomplished the feat three years ago, when the Proteas won all five of their matches in a bilateral series, and the Pakistanis won all three in theirs.