The West Indians, who elected to take first strike in the day-night international on Sunday, lost their last eight wickets for 58 runs after sailing merrily at 80-2 in the 10th over.
Australia, the reigning world number one team, will chase a modest target of 2.8 runs an over under lights at the Brabourne stadium to win the Champions Trophy for the first time in five attempts.
The West Indies, who won the last edition in England two years ago, made a rollicking start as openers Chris Gayle and Shivnarine Chanderpaul plundered 49 off the first five overs.
Chanderpaul, who took 10 runs in Brett Lee's first over, hit 27 off 18 balls when he was bowled by Bracken with the first ball of the sixth over.
Left-hander Gayle, the top-scorer in the tournament with 437 runs from seven previous matches, hit Glenn McGrath for two sixes as he raced to 37 off 27 balls.
Bracken, who had claimed Ramnaresh Sarwan as his second wicket, ended Gayle's hurricane innings when he knocked back the off-stump with a superb delivery that moved in off the seam.
Captain Brian Lara, given a rousing welcome to the crease by some 35,000 Indian fans, plodded for 26 minutes for two runs before falling to a brilliant diving catch by wicket-keeper Adam Gilchrist off McGrath.
Another Gilchrist catch off McGrath removed Runako Morton as the West Indies suddenly found themselves cornered at 94-5 in the 19th.
McGrath, who had conceded 22 runs in his first two overs, gave away just two runs in his next five before being replaced by Shane Watson.
Watson struck in his second over when Marlon Samuels (seven) flicked a catch to Australian captain Ricky Ponting who had stationed himself at mid-wicket for that particular shot.
Australia gained two further wickets off as many balls as Watson trapped Carlton Baugh leg-before with the final delivery of the 25th over and spinner Brad Hogg dismissed Dwayne Bravo (21) in similar fashion in the next over.