Laxman made 148 and Dravid batted the entire third day at Adelaide Oval to reach the close unbeaten on 199, the pair rekindling memories of their famous stand in the "Miracle of Calcutta" Test between the sides two years ago.
They came together after tea on Saturday with India in deep trouble at 85 for four and steered the tourists to 477 for seven, still 79 runs behind Australia's 556 but with the match seemingly heading for a draw.
India added 297 runs for the loss of just three wickets after resuming on 180 for four as Dravid and Laxman demolished Australia's weakened bowling attack on a perfect batting track.
Australia suffered a major setback when fast bowler Brad Williams injured himself while fielding. He was taken to a nearby hospital where scans showed he had strained a shoulder muscle and would not be taking any further part in the match.
Dravid did not offer a single chance in a flawless display to finish one run short of his fourth Test double hundred.
The 30-year-old brought up his 16th Test century after lunch when he hooked Jason Gillespie for six and hit 19 fours to reach the close on 199 after an innings spanning almost nine hours.
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He struck 18 boundaries in an innings spanning 356 minutes off 382 balls before he was dismissed on the last ball before tea, caught by wicketkeeper Adam Gilchrist off paceman Andy Bichel.
Their partnership of 303 was the highest for India in Australia, the two becoming only the third pair in history to complete two triple century partnerships. The others were Australia's Don Bradman and Bill Ponsford and South Africa's Herschelle Gibbs and Graeme Smith.
Fears that India might collapse after the departure of Laxman proved unfounded as the tourists lost just two wickets in the final session, both to part-time spinner Simon Katich.
Wicketkeeper Parthiv Patel was caught by Ponting for 31 and Ajit Agarkar holed to Stuart MacGill for 11.
Photograph: Reuters