Ponting, who was eventually out for 113, reached his century in 85 balls hitting nine fours and five sixes -- his 23rd one-day hundred and fourth in the World Cup.
Opener Matthew Hayden hit a solid 60, while Brad Hogg hitting an unbeaten 15-ball 40 with three sixes and as many fours after Scotland skipper Craig Wright had won the toss and put Australia into bat on a brownish pitch.
Ponting, dropped on 23 by wicket-keeper Colin Smith off medium-pacer Dougie 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 even after a 35-minute rain delay as he broke Indian Saurov 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.
Openers Adam Gilchrist (46) and Matthew Hayden (60) set the foundation for the total by putting on 91 for the first wicket.
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 and was trapped leg-before to 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 tw teams advance to the next round Super Eight.
Fall of wickets: 1-91 (Gilchrist); 2-139 (Hayden); 3-193 (Clarke); 4-256 (Hodge); 5-274 (Ponting); 6-276 (Hussey)
C. Wright (captain), R. Watson, F. Watts, M. Haq, N. Poonia, D. Brown, C. Smith, G. Rogers, J. Blain, G. Hamilton, P. Hoffmann
Umpires: S. Bucknor (WIS) and A. de Silva (SRI), TV umpire: T. Hill (NZL)
Reserve: M. Benson (ENG)
Match referee: J. Srinath (IND)