Ponting hit 123 to steer the tourists away from the first-over dismissal of Matthew Hayden to a more comfortable 254-4 by stumps on the opening day at the Chinnaswamy stadium here.
Ponting, who won the toss and elected to take first strike in good batting conditions, put on 166 for the second wicket with Simon Katich after Hayden was caught behind off the third ball of the match.
Left-handed Katich justified his selection ahead of Phil Jaques by following up back-to-back centuries on the preceding tour of the West Indies earlier this year with a dour 66.
Ponting added 60 for the third wicket with Michael Hussey (46 not out) before he was trapped leg-before by Harbhajan Singh in the final session, the ninth time the Australian captain fell to the off-spinner.
Left-arm seamer Zaheer Khan trapped Michael Clarke leg-before in the day's last over, at which time the umpires called off play.
Ponting set aside a disappointing average of 12.27 in eight previous Tests in India to compile his 36th career Test century, just three behind record holder Sachin Tendulkar's tally of 39.
It was the Australian captain's 200th Test innings, making him only the fourth batsman from his country after Allan Border and the Waugh brothers, Steve and Mark, to achieve the feat.
Ponting's 16th century as captain enabled him to stamp his authority at the start of the four-Test series for the Border-Gavaskar Trophy, which Australia won in India in 2004 and again at home this year with identical 2-1 margins.
The only time Ponting looked in trouble was when India appealed for a return catch as the batsman, then on 110, drove a half-volley back to bowler Anil Kumble, the Indian captain.
With no TV review system in place for the series, umpire Rudi Koertzen consulted his colleague Asad Rauf before turning down the appeal, indicating Ponting had played the ball down into the ground.
The highly anticipated series began in dramatic fashion when Zaheer had veteran Hayden caught behind before the 25,000-strong crowd had settled down.
Pakistani umpire Rauf took time to raise his finger as Hayden stood his ground, but TV replays suggested a faint edge before the ball carried to wicket-keeper Mahendra Dhoni.
Katich's vigil ended just before tea when he poked at a ball outside the off-stump from seamer Ishant Sharma and the edge was easily taken by Dhoni.
Ponting, who was on 94 at tea, reached his century in the first over after the break when he took a four and three off the listless Kumble, who conceded 84 runs in 27 wicketless overs.
Australia left out off-spinner Jason Krejza from the 12 announced on Wednesday to give Victorian leg-spinner Cameron White his Test debut.