Australia looked in the box seat after Head (70 not out) and Carey (49) helped them to 6-291 on a slow wicket before the hosts were barely troubled completing their pursuit with nine balls to spare.
Pathum Nissanka hit his maiden ODI century with 137 in the chase, while Kusal Mendis struck 87 in a 170-run second-wicket stand between the pair before retiring hurt with cramp.
It helped Sri Lanka to their biggest-ever chase against Australia, as they went 2-1 up in the five-match series with back-to-back wins over the tourists for the first time in 20 years.
But beyond this bilateral series, bigger questions continue to remain around Australia’s bowling structure ahead of next year’s World Cup in India.
With Adam Zampa back home on paternity leave, Australia decided not to play Mitchell Swepson.
They were also not helped by a dewy surface at night after initially winning the toss and batting, as the pitch sped up and turned less in the second innings.
Matthew Kuhnemann (0-61 from 10 overs) and Glenn Maxwell were left as Australia’s chief spinners, with Cameron Green (0-31 off five overs) preferred as a pace-bowling allrounder ahead of Swepson.
And where Sri Lanka were able to get great purchase out of their wrist spinner Jeffrey Vanderlay and his return of 3-49, Australia were forced to turn to Marnus Labuschagne (0-49) for seven overs of leg-breaks.
“You can always look back at a lot of decisions and wonder what was the right one,” captain Aaron Finch said.
“We still felt that was the right combination to go for on this wicket with how slow it looked.
“You saw in the first half of the game it was very stoppy and turned quite a bit. We thought it would continue to do that but it played a bit better under lights.”
Pat Cummins was also rested in Sunday’s loss, as Josh Hazlewood and Jhye Richardson bowled tightly but struggled to have pressure built around them.
After Maxwell (1-44) got the only early wicket of Niroshan Dickwella for 25, Hazlewood (1-57) and Richardson (2-39) caused the only other minor damage late.
But by then, the game was gone thanks to Nissanka.
It came after Head had earlier continued his fine form with the bat, hitting an unbeaten 70 from 65 balls just a week after whacking a century for Australia A.
With Steve Smith out and nursing a minor quad strain, Aaron Finch struck 62 and Alex Carey 49 as Australia had to grit and fight their way to a good total.
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