Ponting was forced to pull out of Thursday's warm-up match against South African province Northerns with a hamstring complaint, and Warne had to leave the field after injuring his finger.
Australia won the match by five wickets after stand-in captain Adam Gilchrist and Jimmy Maher smashed half-centuries to help their team overcome Northerns' total of 277.
But the biggest concern for the tournament favourites was the fitness of Warne and Ponting, though both were cleared of any serious problems.
Warne returned to finish his spell after being treated off the field, while a team spokesman told reporters Ponting was only rested as a precaution. He said both were likely to play against Pakistan on Tuesday in the first match of Australia's World Cup defence.
Warne, who has taken 291 one-day international wickets, continued bowling despite bruising one of the fingers on his bowling hand, but was generally ineffective, conceding 70 runs from his eight overs.
Left-handed opener Jacques Rudolph blasted 150 off just 141 balls, smashing 14 fours and six sixes, to help Northerns amass a competitive total.
Fast bowler Brett Lee completed figures of four for 28, including the last two wickets in successive balls, and paceman Jason Gillespie collected two for 31 in a tidy spell.
Australia made a poor start to their reply, losing opener Matthew Hayden for a duck, but they quickly regained control.
Gilchrist struck five fours and five sixes in his typically dashing 64-ball knock of 71, while Maher's unbeaten 78 came off just 80 deliveries.
Andrew Symonds made a rapid 38 to boost his chances of winning the all rounder's spot in the team for the match against Pakistan, and Damien Martyn (31) and Brad Hogg (26 not out) also made valuable contributions.
