Set 170 runs for victory after winning the toss, Australia slumped to a dismal 4-29 inside the powerplay and gave Zimbabwe, 11th on the ICC rankings, reason to dream.
Glenn Maxwell (31 off 32 balls) and top-scorer Matthew Renshaw (65 off 43 balls) spearheaded the rescue mission with a 77-run stand in pursuit of Zimbabwe's 2-169.
But when Maxwell chopped on and last recognised batter Marcus Stoinis (6) holed out, Zimbabwe were on their way to dismissing Australia for 146 with three balls left on Friday.
The shock result leaves Australia fighting to progress out of the group stage. Beating co-hosts Sri Lanka in their next game now appears non-negotiable.
Even with a win in Kandy on Tuesday, Australia could be left to rely on net run rate to qualify for the Super Eight phase.
"We put ourselves under pressure losing wickets in the powerplay," stand-in captain Travis Head said of the upset loss.
"I thought the Zimbabwe boys bowled well and put us under pressure and the scoreboard rate went up.Â
"We found a partnership through the middle but probably left ourselves a little bit too many. That happens, it's disappointing."
The stunning loss came after Australia memorably fell to Zimbabwe in the 2007 edition of the tournament, as well as at the 50-over World Cup in 1983.
Zimbabwe staged their latest boilover without vice-captain Brendan Taylor, sidelined with a hamstring injury, and with captain Sikandar Raza battling calf cramps throughout the fielding innings.
The Zimbabweans did not even qualify for the last T20 World Cup but will now be full of confidence they can progress past the group stage for only the second time.
"The culture, the environment, the unity that we have created over a long time, just to see from outside, I was extremely proud and on top of that, a win," Raza said
"It's just unbelievable."
The bloodshed began in the second over of Australia's run chase as Josh Inglis (8) holed out on the first ball that towering Blessing Muzarabani (4-17) bowled.
Cameron Green and a newly-fit Tim David were caught behind for second-ball ducks to leave Australia reeling at 3-25.
Still deputising for injured Mitch Marsh as captain, Head (17) could consider himself unlucky chopping onto his stumps.
But it nevertheless marked only the second time in history Australia had lost four wickets inside the powerplay at a T20 World Cup.
Batting without a helmet, Maxwell shook off his disastrous recent form and showed flashes of his flamboyant best before also chopping on.
Renshaw, meanwhile, found joy down the ground and notably hit Wellington Masakadza for back-to-back boundaries in the 14th over as Australia staged their fightback.
The No.6 raised his bat for a first T20I half-century in his fifth appearance.
But Australia's key man skied one in the penultimate over facing Muzarabani, who finished with career-best figures and a second-consecutive nod as player-of-the-match.
The wicket of Renshaw left the bowlers with 31 runs required off eight balls.
In a particular highlight of a great day's fielding for Zimbabwe, Tony Munyonga dived in the deep the for a superb catch that dismissed Ben Dwarshuis (6).
Earlier, 22-year-old opener Brian Bennett (64 not out) top-scored for Zimbabwe as wickets proved elusive for Australia.
Stoinis had the first breakthrough in dismissing Bennett's opening partner Tadiwanashe Marumani (35) caught behind, before sending an injury scare through an already depleted Australian camp.
Green (1-6) struck to dispatch of Ryan Burl (35) with the first ball after Stoinis left the field with a hand injury, suffered when Burl blasted a full toss back at him.
Stoinis returned to bat lower down than anticipated at No.7.
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