Carey, bowlers give Australia consolation ODI win over Sri Lanka
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Australia bowled out the hosts for 160, a tricky total on a bowling-friendly Colombo pitch the tourists overhauled with 10.3 overs to spare.
Fast bowlers Josh Hazlewood, Pat Cummins and spinner Matthew Kuhnemann took two wickets each.
Australia were in trouble at 4-50 when the left-handed Carey and Marnus Labuschagne, who made 31, put on a key stand of 51 to set up the chase.
Teenage left-arm spinner Dunith Wellalage took three wickets including David Warner, for 10, and Glenn Maxwell, for 16, but the left-handed Carey kept his calm.
Earlier Sri Lanka slipped to 85-8 before Karunaratne, who improved on his previous ODI best of 44 not out, and debutant Pramod Madushan put on a stubborn stand of 58 for the ninth wicket.
The tourists had quickly rattled the Sri Lankans after Hazlewood removed the openers inside five overs and finished with figures of 2-22.
Charith Asalanka was run out for 14 after a misunderstanding with his partner Kusal Mendis, who made 26 but was out hit wicket off Glenn Maxwell on the next ball.
Kuhnemann, a left-arm spinner, then struck twice in one over including skipper Dasun Shanaka for one as Sri Lanka slipped further to 85-8.
But Karunaratne fought back as he reached his maiden ODI fifty with a boundary off Cummins to celebrate with a fist pump.
Cummins finally got out Karunaratne, who hit eight fours and two sixes in his stay, to wrap up the innings.
In reply, Australia lost skipper Aaron Finch, for nought, off mystery spinner Maheesh Theekshana and the in-form Warner.
Medium-pace bowler Madushan got his first international wicket after he sent back Mitchell Marsh for 24.
Wellalage, 19, got Labuschagne out lbw to break the fifth-wicket stand and then bowled Maxwell to raise hopes of another Sri Lankan fightback.
But Carey stood firm alongside Cameron Green, who made an unbeaten 25, as the pair put together 43 runs to steer the team home.
Many Sri Lankan supporters wore Australia's gold and held banners thanking the tourists for visiting the island nation, which is battling an unprecedented economic crisis.
The hosts bounced back from their opening loss to win three in a row to clinch their first ODI series victory against Australia in more than a decade.
The two teams now head to Galle for two Tests starting June 29.
D. Gunathilaka c Finch b Hazlewood 8
P. Nissanka c Carey b Hazlewood 2
K. Mendis hit wicket b Maxwell 26
D. Chandimal c Finch b Cummins 6
C. Asalanka run out (Kuhnemann/Maxwell) 14
D. Shanaka b Kuhnemann 1
D. Wellalage c Cummins b Kuhnemann 4
C. Karunaratne c Carey b Cummins 75
J. Vandersay run out (Labuschagne) 4
P. Madushan c and b Green 15
M. Theekshana not out 2
Extras (w3) 3
Total (all out, 43.1 overs) 160
Fall of wickets: 1-9 (Nissanka), 2-12 (Gunathilaka), 3-34 (Chandimal), 4-56 (Asalanka), 5-56 (Mendis), 6-61 (Wellalage), 7-62 (Shanaka), 8-85 (Vandersay), 9-143 (Madushan), 10-160 (Karunaratne)
Bowling: Hazlewood 7-3-22-2, Maxwell 10-0-38-1, Kuhnemann 10-3-26-2, Cummins 6.1-1-22-2 (w1), Marsh 1-0-3-0, Labuschagne 7-1-36-0 (w1), Green 2-0-13-1 (w1)
Australia (target 161)
D. Warner c Gunathilaka b Wellalage 10
A. Finch c Asalanka b Theekshana 0
M. Marsh c Nissanka b Madushan 24
J. Inglis c Nissanka b Theekshana 5
M. Labuschagne lbw b D Wellalage 31
A. Carey not out 45
G. Maxwell b Wellalage 16
C. Green not out 25
Extras (w8) 8
Total (6 wickets, 39.3 overs) 164
Fall of wickets: 1-11 (Finch), 2-14 (Warner), 3-19 (Inglis), 4-50 (Marsh), 5-101 (Labuschagne), 6-121 (Maxwell)
Did not bat: P. Cummins, M. Kuhnemann, J. Hazlewood
Bowling: Karunaratne 3-0-19-0 (w1), Theekshana 10-1-26-2 (w4), Wellalage 10-0-42-3 (w2), Vandersay 9.3-0-46-0, Madushan 3-0-13-1, Asalanka 4-0-18-0 (w1)