Chigumbura finished on 52 not out and shared an unbroken stand of 55 with Prosper Utseya as Zimbabwe chased down a target of 210 to win with two overs to spare.
Zimbabwe's only previous win over the Australians was at Trent Bridge in the 1983 World Cup, in the first ever encounter between the two sides.
Sunday's defeat was a humbling experience for Australia, who misread conditions and left out legspinning all rounder Steve Smith, and underestimated Zimbabwe by resting premier fast bowler Mitchell Johnson.
"At the end of the day the selectors pick the team and I try and get the best out of the players," Clarke said.
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"That's all you can do. I think we've seen through Smithy's career that he's a pretty good player of spin bowling and he can bowl some handy leg spinners, so I think he would have been handy out there."
Australia now need to beat South Africa on Tuesday to assure themselves of a place in Saturday's final.