Clarke brought up his second double century of the series after his unbeaten 329 in the Sydney test just before lunch with two runs through mid-wicket, celebrating with his ritual kiss of the insignia on his helmet.
The 30-year-old took 361 minutes and 255 balls to reach the milestone with another imperious display, which included 25 fours and one six.
Ponting was not far behind but was forced to wait nervously over the lunch break for his second double century against India at Adelaide after the 242 he hit in a losing cause in 2003-04.
The sixth double century of his career finally came courtesy of a trademark pull to midwicket for his 21st four in the 459-minute, 357-ball innings and the celebration left no doubt what it meant to the Tasmanian.
Clarke had already departed after being bowled between bat and pad by paceman Umesh Yadav, the first wicket to fall in more than three full sessions.
The stand was two runs short of the Australian record for a fourth-wicket partnership set by Donald Bradman and Bill Ponsford when they made 388 at Headingly in 1934.
In Image: Australia's Ricky Ponting, left, celebrates his double century with teammate Mike Hussey