Beaten by India and South Africa in the first two matches, Australia showed some urgency with the ball and bundled out Sri Lanka for 209 inside 44 overs with Adam Zampa leading the rout on figures of 4-47.
At 157-1 near the halfway stage, Sri Lanka looked poised to reach the 300-mark before the wheels came off their innings and they had to settle for a below-par total.
After strong winds delayed the start of their chase, Australia made heavy weather of a small target before Josh Inglis made 58 and Glenn Maxwell (31) stayed put to see them home with nearly 15 overs to spare.
It was Australia's first victory in the tournament, while 1996 champions Sri Lanka remained winless after three matches.
"We didn't say much before the game, but after two losses we wanted to get back to where we know we can be with our high standards," Australia captain Pat Cummins said.
"Their openers started really well and we were staring down the barrel of a big score.
"But we stuck together, all our bowlers did their job and to finish it off for 209 was a great effort."
Sri Lanka played under a new captain, Kusal Mendis, after Dasun Shanaka's tournament was cut short by a thigh injury.
Mendis elected to bat after winning the toss and a 125-run opening stand between Pathum Nissanka (61) and Kusal Perera (78) appeared to vindicate that decision.
David Warner grabbing two stunning catches to dismiss Nissanka and Mendis while Cummins removed Perera before the bottom half of Sri Lanka's batting order caved in.
Strong winds knocked off a couple of banners in the stadium and when play belatedly resumed Dilshan Madushanka rattled Australia with a two-wicket maiden over.
A fuming Warner (11) left the field resenting the lbw decision against him but Steve Smith looked plumb in front.
Marsh raced to a 39-ball fifty to ease some of the pressure but eventually perished in pursuit of a risky second run.
Marnus Labuschagne was given caught behind to the first ball but the decision was reversed after replays confirmed it had come off his thigh pad.
Labuschagne fell for 40 but Inglis could not be denied his fifty.
Inglis fell after a run-a-ball knock while Maxwell smashed two sixes and four fours in his 21-ball cameo before Marcus Stoinis sealed the victory with a six.
"Pathum and KP (Kusal Perera) batted well for the opening partnership but after that the middle order struggled," said Mendis.
"If we could score 290-300, it would have been a good total on this pitch."
