The day was made even more painful for Australia's Steve Smith (92) and Mitchell Starc (99), who both fell narrowly short of scoring their maiden Test hundreds.
Dhawan's century included an amazing 21 fours.
The left-hander looked in complete command from the outset, after coming into the side as a replacement for dumped veteran Virender Sehwag.
"The wicket is offering nothing,'' Australia pace bowler Starc said after taking 0-46 from his 11 overs.
"They've batted very well. It's a very flat wicket and there's nothing in it for the quicks.''
Despite all the dramas of `homeworkgate', the criticism from ex-players back home and the wicket-less day in the field, Starc said the mood in the change rooms was not too bad.
Starc saw a positive in the fact India had been 1-387 in their first innings of the second Test and were bowled out for 503.
"We didn't take a wicket in that big partnership (on Saturday of 283) but we saw in the last Test they had a big partnership (of 370 for the second wicket) and then lost nine for only a hundred odd,'' Starc said.
"There's no reason we can't do that again here and come back tomorrow, bowl in partnerships and make sure we're very patient.''
Earlier, Australia relied on a lower-order fightback to produce their highest score of the series after being 7-251.
No.5 batsman Smith and No.9 Starc shared a crucial 97-run stand for Australia's eighth wicket.
The homeworkgate affair which sent shockwaves through world cricket on Monday presented Smith with the chance to play his first Test since January 2011.
The energetic 23-year-old grabbed it with both hands.
India lead the four-match series two-nil and Australia's hopes of avoiding a four-nil whitewash appear slim. The home side are well-placed to push for victory despite a washout on day one.
Test batsman Shane Watson, reserve batsman Usman Khawaja and pacemen James Pattinson and Mitchell Johnson were handed one-match suspensions by Australia coach Mickey Arthur for failing to complete a homework assignment on time.
All could come under consideration for the Delhi Test on March 22.
- AAP