The visitors had scored 250 runs in their first innings.
Inclement weather first delayed play by 45 minutes in the morning session, and then there were two more delays in the first session before lunch was taken at 1.12 pm local time.
During the first 20 minutes of play, starting from overnight 191 for seven, Australia crossed 200 in the 91st over but India managed to sneak in a breakthrough before rain came again. Mitchell Starc (15) was caught behind off Jasprit Bumrah (3-47) as covers came on.
Play was held up for 55 minutes thereafter, and the number of overs for the day were reduced to 79. On resumption, the remaining one-hour session was cut short again after 40 minutes but this time India made good used of the overs.
Both Bumrah and Ishant Sharma (2-47) were guilty of bowling shorter to the tail-enders, and it didn't change this morning either. Nathan Lyon (24 not out) made good use of this, hitting two fours and a six, as he put on 31 runs for the ninth wicket with Travis Head (72).
Head's immaculate knock came to an end when he edged Mohammed Shami (2-58) behind, and the very next ball, the pacer finished things off with Josh Hazlewood out caught similarly for a first-ball duck.
Wicket-keeper Rishabh Pant finished with six catches, while Head faced 167 deliveries in all, inclusive of six fours.
Australia were happier of the two sides having added 44 runs in just 10.4 overs of play. In their bid to get the lower order out quickly, India were guilty of leaking easy runs.
An early lunch was taken at the last rain interval.
On day one, Cheteshwar Pujara's 16th Test century saved India the blushes. On day two, the Indian bowling attack worked hard to restrict the Australian batsmen with Head the only one to cross the 50-mark.