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.
Sri Lanka skipper Mahela Jayawardene said subsequently Murali was nursing a groin problem and Vaas needed a break.
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 Austra