Australia, who were chasing a target of 237, were in control until losing five wickets for 42 runs to be restricted to 224 off their 50 overs.
Taylor, the 22-year-old Jamaican, clean bowled Michael Hussey and trapped Brett Lee leg-before with the last two balls of his ninth over, the 48th of the innings.
The 22 year old then returned for the final over with Australia needing an improbable 16 runs and shattered Brad Hogg's stumps with his first delivery to complete a split hat-trick.
Taylor finished with 4-49 to stop Australia, who were cruising at 182-4 in the 42nd over following a 101-run stand between Adam Gilchrist (92) and Michael Clarke (47).
But the loss of Gilchrist's eight runs short of a deserved century triggered a collapse in which the unusually tentative Australians lost their last three wickets in the space of five runs.
Hugs all round for the Windies
The unexpected defeat continued Australia's jinx in the Champions Trophy, which they have never won despite taking home the last two World Cups in 1999 and 2003.
Once again it was Captain Brian Lara who played a pivotal batting role for his side.
He joined Runako Morton for a fifth wicket partnership of 137, which steered the West Indies away from disaster after they stalled to be 63-4 at the 15th over.
The legendary West Indian batsman dropped himself to number six, but showed some of his vintage form on the way to 75, while Morton went even further to remain unbeaten with 90.
The wicket at the Brabourne stadium played far better than the one slammed by South African captain Graeme Smith, and while it wasn’t a batters paradise Lara, Morton, Gilchrist and Clarke all showed there was some value in it.
Australia play England next in Jaipur on Saturday. The West Indies take on hosts India in Ahmedabad on October 26.