Their top three batsmen, David Warner (69), Shane Watson (66) and Peter Forrest (53), all made half-centuries, to set the platform for a big total.
But the West Indian bowlers did a good job of restricting Australia to under 300, conceding less than 70 runs in the last 10 overs, with Andre Russell capturing four wickets and Kemar Roach three.
"At one time it looked like we would be chasing 330 but we pulled it back," West Indies captain Darren Sammy said at the post-match presentation.
"Against the world number one (ranked team), with our backs against the wall, it was fantastic effort from the team.
"We have a 'never say die' attitude, everyone played their part, as a captain I was well supported and it's good to see us getting results."
Sammy top-scored for West Indies with a defiant 84 before he was the last man out and the home side were dismissed for 251 in the 48th over.
Opener Adrian Barath made a patient 42 but got little support from the West Indian top order with Johnson Charles and Marlon Samuels both failing to score and Darren Bravo making just three.
"It was good for us in the end, to close off the game, even though a fantastic innings from Darren Sammy ran us close," said Australia skipper Watson.
"We are in a bit of a transition phase, it's been a pleasing series, there are a few things we have to work on but we're going the right way."
The five-match series ended level at 2-2 after Australia won the first and last match and West Indies claimed victory in the second and fourth. The third game ended in a tie.
The teams will play two Twenty20s, starting on Tuesday, before three tests.
"I think we should have won the series," said West Indian allrounder Kieron Pollard, who was named player of the series.
"Both teams played well but I think we have won back some of the hearts of the people of the West Indies."