Returning captain Mitch Marsh and a revived Travis Head looked to have set Australia on course for a victory that would have kept their tournament hopes alive as they smashed a century-plus opening stand at more than two-runs-a-ball.
But after Head was dismissed the innings collapsed with Australia losing ten wickets for 77 in 70 balls.
Nevertheless, though bowled out for 181 off the last ball, Australia still set a record chase for Sri Lanka at home, which looked even more daunting after recalled opener Kusal Perera was dismissed early on.
But Pathum Nissanka scored a brilliant 52-ball unbeaten 100 as the co-hosts made light of the challenge, winning by eight wickets with two overs to spare.
The result put Sri Lanka into the Super Eights. If Zimbabwe beat Ireland on Tuesday (2030 AEDT) Australia are out of the World Cup. Even should Zimbabwe lose Australia need them to be beaten by Sri Lanka on Thursday (2030 AEDT).
If Zimbabwe do lose both matches Australia then need to beat Oman on Friday (Saturday 0030 AEDT), and do so convincingly enough to finish above the African side on net run rate.
"We are in the lap of the Gods now," said Marsh. "We will watch the Zimbabwe-Ireland game with hope, but it is a devastated group. There's a lot of emotions in the room. We have not been at our best.
"Sri Lanka outplayed us. We know at our best we can make big scores. We just lost our way towards the back end. Could not get a partnership going and they bowled really well. Coming off we knew we were a bit short with the start we had."
Australia's batting was an innings of two parts. For the first 50 balls Australia were dominant as Marsh and Head put on 104 against an attack that lost seamer Matheesha Pathirana with a calf injury four balls into his opening over.
Marsh, playing his first match of the tournament after suffering a testicular injury, highlighted the top order verve Australia have been missing with eight fours, including five in succession off Maheesh Theekshana to end the powerplay, and a six.
Head had made 50 runs combined in his past four innings, but he reached that landmark in 27 balls with a brutal display of hitting, posting seven fours and three sixes.
But in mid-innings the spinners changed the game. After Head was caught on the boundary for a 29-ball 56 wickets tumbled and the rate slowed.
From 0-104 Australia slumped to 4-130 with Marsh among them, lbw on review for a 27-ball 54.
Head's exit had brought in Green but he was quickly stumped. With scores of 21, 0 and 3 in the competition he was a contentious selection given the arrival of Steve Smith and the good form of Matt Renshaw. The Queensland batter made way for Marsh despite being top scorer with 65 in the shock loss to Zimbabwe that had put Australia under pressure to win this match.
It could have been worse. Josh Inglis, who was the third best score with 27, should have been stumped first ball.
His eventual departure, after Glenn Maxwell (22) had been superbly caught by Nissanka reverse sweeping, prompted another clatter of wickets, the last five going down for seven runs in 12 balls.
It still looked a testing target and Australia made an early inroad when Stoinis had Perera caught at deep point. But Nissanka and Kusal Mendis added 97 off 66 balls to keep the match in the balance.
It took the return of Stoinis to break the partnership, Mendis caught by Connolly at deep mid-wicket for a 38-ball 51.
But that was as good as it got for Stoinis. The new batter, Pavan Rathnayake (28no off 15), carted his first two balls for four and 20 were taken of Stoinis' next over, the 15th.
That brought the target down to 41 off five overs. Sri Lanka only needed three with Nissanka completing a majestic century off what proved the penultimate delivery.
31°C