Zimbabwe first restricted Australia to 138 for nine and then sneaked home with one ball to spare in a thrilling contest.
Zimbabwe needed 12 runs in the last over bowled by Nathan Bracken. Taylor hit the first ball for four and squeezed out four more runs along with Chigumbura off the next three balls before gaining four leg byes in the penultimate ball to trigger celebrations in the Zimbabwe camp.
Earlier, Elton Chigumbura picked up three wicketsin a  disciplined Zimbabwe bowling performance.
Electing to bat under overcast conditions, the ODI world champion Australian side kept losing wickets at regular intervals after a top-order collapse.
The Zimbabweans, on the other hand, put up an inspired performance to give themselves a chance of an upset win.
After brief spell of rain delayed the start of play by a few minutes, Australian openers Adam Gilchrist and Matthew Hayden departed in quick succession on a seaming track.
Both the batsmen made just four runs each before leaving the Aussies reeling at 12 for 2. While Hayden edged a Chigumbara delivery to wicketkeeper Brendon Taylor, Gilchrist holed out to Stuart Matsikenyeri while attempting a pull off the same bowler.
Skipper Ricky Ponting (8) followed the duo back to the pavilion soon as he gave an easy catch to Chigumbura by trying to swing Gary Brent. Andrew Symonds and Mike Hussey then steadied the innings for a some time but disaster struck soon as the latter was run out at 15.
A moment of indecision from Hussey was all that Vusi Sibanda needed as he dived full stretch to hit the stumps directly with the Aussie left-hander fell just short of his crease.
Symonds (33) could not stay for long either as Taylor displayed some excellent glovework to stump the right-hander and end his brief partnership with Brad Haddin (6).
The Aussie scorecard read 102 for six with just 3.4 overs remaining before Brad Hodge’s unbeaten 35 helped the world champions to 138 for nine.
SCORE BOARD
Australia
Gilchrist c M’kenyeri b C’bura 4
Hayden c Taylor b Chigumbura 4
Ponting c Chigumbura b Brent 8
Symonds st Taylor b Masakadza 33
Hussey (run out) 15
Hodge (not out) 35
Haddin c Chigumbura b Utseya 6
Lee b Brent 12
Johnson (run out) 9
Bracken c Sibanda b Chigumbura 4
Extras (B-2, W-6) 8
Total (for 9 wkts; 20 overs) 138
Fall of wickets: 1-7, 2-12, 3-19, 4-48, 5-86, 6-102, 7-119, 8-134, 9-138.
Bowling: Chigumbura 3-0-20-3; Brent 4-0-19-2; Mupariwa 3-0-23-0; Chibhabha 3-0-17-0; Utseya 4-0-28-1; Taibu 2-0-20-0; Masakadza 1-0-9-1.
Zimbabwe 
Sibanda c Gilchrist b Bracken 23
Taylor (not out) 60
Chibhabha c Gilchrist b Clark 15
Taibu c Gilchrist b Johnson 0
Matsikenyeri c Gilchrist b Clark 3
Masakadza lbw b Lee 27
Chigumbura (not out) 4 
Extras (LB-4, W 3) 7            
Total ( for 5 wkts; 19.5 overs) 139
Fall of wickets: 1-31, 2-54, 3-55, 4-70, 5-123. Bowling: Lee 4-0-31-1; Bracken 3.5-0-25-1; Clark 4-0-22-2; Johnson 4-0-26-1; Symonds 2-0- 11-0; Hodge 2-0-20-0.