Spinner Adam Zampa led the bowling with four wickets in Australia's five-wicket win on Monday but it was Cummins who unlocked the Sri Lankans after openers Pathum Nissanka and Kusal Perera put on a century stand.
Cummins banged in a short ball to remove Nissanka for 61, with David Warner assisting with a brilliant catch, before the captain bowled Perera for 78 with a fine delivery that extracted movement from a largely tepid pitch.
Cummins then produced an inspired piece of fielding to run out Dunith Wellalage for two as Sri Lanka were bowled out for 209 and easily picked off by the Australian batters.
With Cummins managing a total of one wicket from twin thrashings by India and South Africa, former Australia captain Michael Clarke caused a media storm back home when he told local radio that the skipper was set to be dropped against Sri Lanka.
The very idea of Cummins being on the chopping block was mystifying to legspinner Zampa, who was adamant there was no heat coming from within the team.
"I thought Cummins's spell in particular was a bit of a game changer for us and even his energy in the field, the run-out after the rain-break, yeah, it changed the energy for us," Zampa told reporters.
"We all back each other 100% in this team, so I don't really know what's been said or what people are reading, but the only thing that I saw come on the WhatsApp group was same 11 as last game.
"So, yeah, there's no pressure on Pat there."
The win lifted Australia off the bottom of the World Cup standings before they take on Pakistan, who lie fourth, in Bengaluru on Friday.
Opener Travis Head has been sorely missed while nursing a broken left hand, and while on track to rejoin the squad this week he is not expected to be fit for Pakistan.
Opening in Head's place, all-rounder Mitchell Marsh also had a welcome return to form with a half-century against the Sri Lankans after making a total of seven runs in the previous two matches.
Zampa said the mood had been "flat" in the changing room after the first two losses but things could change quickly.
"We get backed into a corner and guys step up and we get on a roll, then anything can happen," he said.
"It's a World Cup, so get on a roll.
"Obviously, really big game against Pakistan in Bangalore, and if we can put it all together and play a good game there, you go two (wins) and two (losses) and the feeling's much better."
