The duo had also scored half-centuries in their team's seven-wicket win in the previous match.
Fast bowler Doug Bollinger led Australia's disciplined attack with three wickets to restrict Sri Lanka to a modest total before Ponting and Clarke ensured victory with their 107-run stand.
"It was a fantastic innings from Ricky," said Clarke.
"The bowlers did a great job. They are executing their plans really well. Full credit to them."
Clarke, playing his 200th one-day international, hit two sixes and four boundaries in his 67-ball knock.Ponting also added 94 for the second wicket with in-form opener Shane Watson (43) after the early dismissal of Brad Haddin.
"The game was set up by our bowlers who kept taking wickets," said former captain Ponting, who was named man of the match.
"I am getting a few runs, so not being captain must be working all right."
Watson, who became the first batsman to complete 1,000 runs in one-dayers this year, was bowled by paceman Lasith Malinga after hitting one six and four boundaries in his 51-ball knock.
Bollinger was earlier superbly backed by fast bowlers Mitchell Johnson and Brett Lee, who bagged two wickets apiece.
"It was not a great day for us," said Sri Lanka captain Tillakaratne Dilshan.
"We didn't get enough runs. This was a 250 pitch. We have to work things out as a batting unit. Ponting and Clarke batted really well."
Former captain Kumar Sangakkara top-scored for Sri Lanka with a patient 52, hitting just one six and one four in his 85-ball knock. He added 63 for the fifth wicket with Angelo Mathews (35).
Lower-order batsman Nuwan Kulasekara helped Sri Lanka cross the 200-mark with a brisk 31-ball 34.
Sangakkara fell just when he looked like stepping up the run-rate, caught by Johnson at long-on while attempting a big shot off spinner David Hussey in the 37th over.
Australia gained the upper hand when they reduced Sri Lanka to 77-4, with Lee, Johnson, Bollinger and left-arm spinner Xavier Doherty taking one wicket each.
Dilshan (24), Mahela Jayawardene (17) and Upul Tharanga (13) all got starts, but none could play a big knock.