Australia elected to bat first and Jess Cameron's 75 off 76 balls helped them post a score of 259/7.
Barbados' Shaquana Quintyne, 17, took 3/34 as Australia threw away a good start, floundering in the final powerplay overs.
Openers Meg Lanning (31) and Rachael Haynes (52) got their team off to a rollicking start, reaching 52 runs in just nine overs. After the fall of Lanning, Haynes strung together a partnership of 64 runs with Cameron to put Australia in the driver's seat.
Cameron, named player of the match, was in delightful touch as she carted the West Indies bowlers all around the ground in an innings that included eight fours and two sixes. With the score on 177/3 at the end of the 35th over, Australia looked well on their way to post a big score.
However, things took a turn for the worse with the start of the batting powerplay. Reckless batting saw Australia being reduced to 192/6 by the 40th over. Leg spinner Quintyne bowled well and reaped the dividence of poor shot selection.
Australia regained the initiative in the end thanks to some lusty blows by captain Jodie Fields (36 not out) and Ellyse Perry (25), who had a partnership of 50 runs for the eighth wicket and helped them push the score past the 250-mark.
Coming out to bat, the West Indies women never looked to dominate the girls from Down Under as the latter kept on taking wickets at regular intervals. Chasing a target with the run-rate of 5.18 runs per over, the West Indies batters failed to deliver.
Medium pacer Perry also shone with the ball as she ripped through the West Indies top order. Perry finished with the best figures of the match, 3/19 in 10 overs. Erin Osborne (2/26), Lisa Sthalekar (2/20) and Megan Schutt (2/38) chipped in with two wickets each to deny the West Indies women to go past the 150-mark.
West Indies skipper Merissa Aguilleira top scored with 23.
The West Indies, who reached their first ever World Cup final here, had earlier defeated Australia in the Super Sixes.
New Zealand's Suzie Bates, who scored the most number of runs in the tournament (407), was named the player of the tournament.