Ponting lofted five sixes and struck nine fours in his 113 from 93 balls, his 23rd international one-day century. He also broke Indian Saurav Ganguly's previous World Cup record of 23 sixes and became the sixth man to reach 1,000 World Cup runs.
Scotland captain Craig Wright ensured the spectators, who filled less than half of the 10,000-capacity Warner Park, would get a decent day's cricket by opting to field first after winning the toss on a dull, overcast day.
Paul Hoffman, who had last played against Adam Gilchrist 20 years ago when he represented Queensland Schools against New South Wales Schools, beat his old adversary outside the off-stump in a useful opening over.
Matthew Hayden, returning to the side after breaking his right toe while scoring an Australian record 181 not out against New Zealand, was off the mark with a firm push through mid-wicket for four off Hoffman and Gilchrist slashed the former Queenslander for an uppish boundary over point.
Hayden showed his intent by marching down the pitch to loft Hoffman for a brutal six over long-on in the seventh over and the pair brought up their 50 partnership from 46 balls.
Gilchrist was four short of what would have been a somewhat streaky half-century when umpire Steve Bucknor adjudged him lbw trying to swing former England one-day all-rounder Dougie Brown's enthusiastic medium-pace to leg. He had hit seven fours from 55 balls
Ponting reached 1,000 World Cup runs when he pushed Brown sweetly through mid-on for four. He accumulated 23 without undue fuss when he was dropped by wicketkeeper Colin Smith standing up to the stumps from a thick outside edge off Brown.
Hayden passed his half-century but was out lbw for 60 pushing forward to Majid Haq in the off-spinner's first over after striking six boundaries and a six from 73 deliveries.
Ponting hit Haq for six over long-on to bring up the 150 and danced down the pitch in the next over from left-arm spinner Glenn Rogers, another former Queenslander, to strike another six.
By now nothing the Scotland bowlers could do was troubling Ponting, who lofted two further sixes off Haq and Rogers.
He lost Michael Clarke (15) and Brad Hodge (29) either side of a 30-minute rain break and smashed one further six after reaching his hundred from 85 balls before he was bowled by Wright.
Michael Hussey made only four but a late assault by Shane Watson (18) and Brad Hogg (40 off 15 balls) took Australia past 300.
Australia 334 for 6 in 50 overs (Ponting 113, Hayden 60, Gilchrist 46, Hogg 40 n o; Rahim ul-Haq 2 for 49, Rogers 1 for 52) Vs Scotland (yet to bat)