Sent in to bat, to the crowd's short-lived delight, Australia slumped to 141 all out in 31 overs with a counter-attacking 94 from 96 balls by David Warner the only major contribution.
Australia's bowlers tried admirably to defend the low total, but visiting captain Regis Chakabva (37 off 72 balls) ensured his side secured an unlikely upset, only their third ODI win against the home side, reaching 142-7 in 39 overs.
In tricky morning conditions, Aaron Finch's wretched run of form showed no sign of abating. He added five before being caught at second slip off the bowling of seamer Richard Ngarava, who accounted for the Australia skipper in all three matches.
Wickets tumbled on the two-paced surface and Australia slid to 72-5 when left-arm spinner Sean Williams had Cameron Green caught for three.