The Australian skipper notched a 93-ball, 113 to propel the defending champions to 334-6 before the Aussie pace attack proved too hot for the minnows who were bowled out for 131 in 40.1 overs.
"It was a good game and a good hit out today. We beat England last week, we've been playing some good cricket in recent weeks," said man-of-the-match Ponting.
Scotland skipper Craig Wright said he was proud of his team.
"We competed well for the first 45 overs of their innings, but the last five of theirs and the first 10 of ours killed us," said Wright after Australia had plundered 50 runs off the last 22 balls.
"But we stuck at it. It wasn't easy on a small ground against a top-class outfit."
Ponting, who shrugged off a 35-minute rain delay, was eventually out in the 46th over.
He reached his century in 85 balls hitting nine fours and five sixes -- his fourth in the World Cup.
The Scots then lost half of their side within the first 16 overs, with McGrath taking three of the wickets.
The lanky 37-year-old paceman had Fraser Watts in his second over, then accounted for Ryan Watson in his third and Gavin Hamilton in his fourth to leave the Scots reeling at 42-5 by the 16th over.
Colin Smith (51) and Dougie Brown (19) shared 47 for the sixth wicket to give the Scots' total some respectability.
Australia recorded the biggest World Cup victory when they defeated Namibia by 256 runs at Potchefstroom in 2003.
McGrath, who started the tournament ten wickets short of equalling Pakistan's Wasim Akram's all-time World Cup record of 55 victims, finished with 3-14 off his six overs.
Earlier, Ponting, dropped on 23 by wicket-keeper Smith off paceman Brown, took full advantage of the lapse and added 54 runs for the third wicket with Michael Clarke (15) and another 63 for the fourth with Brad Hodge (29).
Ponting never lost his rhythm as he broke Indian Sourav Ganguly's previous World Cup record of 23 sixes and became the sixth man to reach 1,000 World Cup runs.
Ponting is playing in his fourth World Cup.
Opener Matthew Hayden hit a solid 60, while Brad Hogg hit a fiery unbeaten 15-ball 40 with three sixes and as many fours to deliver the final blow after Craig Wright had won the toss and put Australia into bat on a brownish pitch.
Hayden set the foundation for the total by putting on 91 for the first wicket with Adam Gilchrist who made 46.
Hayden hit six boundaries and a six before he fell leg-before to off-spinner Majid Haq who was the pick of the Scottish bowlers with 2-49.
Gilchrist hit seven boundaries before he was trapped leg-before by Brown who bowled well before conceding 24 runs in his final over to Hogg.
South Africa and the Netherlands, the two other teams in the Group, meet on Friday. The top two teams advance to the next round Super Eights.