Needing 116 from 35 overs after rain stopped play for more than two hours, Australia cruised home in the 29th over at the Brabourne stadium in Mumbai on Sunday.
The defending champions, fielding seven players who played in the last tournament two years ago, collapsed to 138 all out after charging to 80-2 in the 10th over on a slow wicket.
Australia's left-arm seamer Nathan Bracken took three wickets for 22 runs as the West Indies lost their last eight wickets for 58 runs.
Australia started slowly slipping to 13-2 in the fourth over. Adam Gilchrist was caught in the slips by Chris Gayle off Ian Bradshaw for two and Ricky Ponting was out lbw to Jerome Taylor for no score.
But Damien Martyn and Shane Watson took the world champions home with an unbroken third-wicket stand of 103 on either side of the rain interruption.
Watson was declared the man of the match after his unbeaten 57.
Rain stopped play for more than
two hours during the final
"It is a great feeling to win a tournament as big as this," Ricky Ponting, the Australian captain, said.
"This is the one we hadn't won. Full credit to all the guys for the way they played and applied themselves over the last month. When the big games come around, we put our hands up and perform."
West Indian captain Brian Lara, who managed just two runs in 26 minutes at the crease before falling to a brilliant diving catch by wicket-keeper Adam Gilchrist, complemented his team for reaching the final but said they were overawed by the world champions.
"We worked hard to get here so it is obviously a bit disappointing that we did not do well today," he said.
"Maybe it was a bit of stage fright. But the boys have started to believe in themselves and this will hold us in good stead for the World Cup we host in March."
Australia now return home to prepare for the Ashes series against England which starts in Brisbane on November 23.