Australia, chasing a West Indian total of 236-6 under lights at the Brabourne stadium, lost five wickets for 42 runs to be restricted to 224-9 in 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.
Taylor 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 Gilchrist's run out 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.
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.
It was the first match for both teams in the main tournament. England and hosts India are the other two teams in group A where the top two will qualify for the semi-finals.
The West Indian innings revolved around fluent half-centuries from captain Brian Lara and Runako Morton.
The pair added 137 for the fifth wicket after the West Indies, electing to take first strike on the dry wicket, were reduced to 63-4 by the 15th over.
Lara, who dropped himself to number six, made up for a hesitant start to flay two sixes and seven boundaries off the world champions in his 71 before hurting his back while playing a shot.
He called for treatment soon after smashing fast bowler Brett Lee for a six and managed to add only four more runs before spooning a catch to the covers off Glenn McGrath.
Morton remained unbeaten on 90, a knock studded with seven fours and a sweetly-timed six over long-on against McGrath in the penultimate over.
The centre wicket at the Brabourne stadium played better than the controversial dusty side tracks provided for the previous two matches that were described as "sub-standard" by South African captain Graeme Smith.
The ball still did not come on to the bat to facilitate strokeplay, forcing the batsmen to grind for their runs. But batting was not a difficult task as Lara, Morton, Gilchrist and Clarke showed.
The West Indies, bowled out for 80 by Sri Lanka in the final qualifying match here last week, recovered to hold their own after a shaky start against the spot-on Australian bowling.
The Australians themselves began on the wrong foot as they slumped to 81-4 before Gilchrist and Clarke retrieved the situation.
The injured Lara cheered from the dressing room as his team-mates fought back in dramatic fashion to seal a superb victory.
Australia play England next in Jaipur on Saturday. The West Indies take on hosts India in Ahmedabad on October 26.