Australia had a minor wobble when occasional off-spinner Russel Arnold took two wickets in five balls to leave them 79 for two.
But Ponting and Andrew Symonds (63 not out) saw Australia, chasing 227 to win, to 232 for three with an unbroken stand of 106 in a win achieved with 44 balls to spare when the captain hit leg-spinner Malinga Bandara for six.
However, Sri Lanka's attack was missing fast bowler Lasith Malinga (ankle ligaments) and the rested duo of left-arm quick Chaminda Vaas and off-spinner Muttiah Muralitharan.
Between them the Sri Lankan trio had taken 41 wickets at this tournament, Vaas and Murali bagging three apiece in the six-wicket win against New Zealand last time out which Malinga also missed through injury.
Both sides had already qualified for the semi-finals and Sri Lanka's decision to omit 1996 World Cup winners Vaas and Murali denied Australia's batsmen fresh experience against the pair ahead of a possible final clash - the teams are set to avoid one another in the last four.
Ponting's fifty came off 67 balls with three boundaries while Symonds, in typical hard-hitting form, reached the landmark in 56 balls with two sixes and three fours.
Before this match Ponting said he'd expected a "hard, honest contest" but the selection policy of Sri Lanka, coached by former Australia international Tom Moody, gave his side a huge advantage before a ball had been bowled.
However, it needed a key double strike from left-arm wrist spinner Brad Hogg to spark a collapse as Sri Lanka were bowled out for 226.
Sri Lanka, after slumping to 27 for three, saw captain Mahela Jayawardene (72) and Chamara Silva (64) put on 120 for the fourth wicket before both batsmen fell in quick succession to Hogg, who took two wickets for 35 runs from his 10 overs.
Left-arm quick Nathan Bracken did a superb job at both ends of the innings in a miserly return of four for 19 from 9.4 overs.
Sri Lanka, from 167 for three, lost their last seven wickets for 59 runs.
Their attack then needed every chance to go to hand.
But Arnold, fielding close in at short cover, put down a tough head-high catch when Adam Gilchrist was on 10, off Dilhara Fernando.
Matthew Hayden, characteristically aggressive, drove Farveez Maharoof for six. But a partnership worth 76 in under 12 overs was broken when Hayden, on 41, dragged Arnold's fifth ball to Tillakaratne Dilshan at mid-wicket.
And 76 for one became 79 for two when left-hander Gilchrist missed Arnold's quicker ball and was lbw for 30.
Even when Michael Clarke (23) fell to Bandara, Australia were in charge at 126 for three in the 24th over.
Sri Lanka had to face Australia's first-choice attack and, after Jayawardene won the toss, they lost three wickets lost for one run in 14 balls.
Veteran opener Sanath Jayasuriya was lbw for 12 to Bracken.
Then Glenn McGrath needed just three balls to strike when Kumar Sangakkara fell lbw for nought.
Jayawardene countered, hooking fast bowler Shaun Tait for a six that brought up his fifty in 64 balls, and a century stand with Silva, whose half-century came in 91 deliveries.
But Hogg ended the partnership when Silva top-edged a sweep to Clarke at short fine-leg.
Then 167 for four became 174 for five when Jayawardene was stumped off Hogg by wicket-keeper Gilchrist as he played for turn.
Sri Lanka's last Super Eights match is against surprise package Ireland here Wednesday while Australia's second round programme ends at the National Stadium on Friday against fellow semi-finalists New Zealand.