Dropped catches, India's dominance and a docile pitch compounded Australia's misery at the MCG, where the tourists declared at 7-443 late on day two of the Boxing Day Test.
Make-shift opener Hanuma Vihari did not make many runs, getting just 8 off 68 balls in his 40-run stand with Agarwal but they batted out 18.5 overs, India's longest opening stand in terms of balls faced in Test cricket across Australia, New Zealand, England and South Africa since December 2010.
The duo added unbeaten 92 runs in the third session.
Starc, Cummins and Josh Hazlewood have already delivered a combined 84 overs in the match.
The inaugural Test at the Optus Stadium saw Virat Kohli, Marcus Harris, Aaron Finch, Nathan Lyon and Umesh Yadav struck with vicious bounce, though none were seriously hurt. Kohli - who came out to face the first ball post tea break - looked in cruise control early on.
India played through a near carbon copy of day one, scoring at little over 2.5 runs an over before declaring at 7/443 half an hour before stumps.
Cheteshwar Pujara's 319-ball 106 was finally ended by a Pat Cummins delivery which stayed unsually low and skidded on to off-stump. The bowlers, however, continued to bowl dry lines and lengths allowing India to score only 62 runs on the second morning.
Pat Cummins (40/2) was Australia's best, although it was mostly short-pitched bowling that looked unsafe.
With the four-Test series tied 1-1, much is riding on the Boxing Day showdown at the Melbourne Cricket Ground where up to 90,000 fans are expected, and India can't afford another top-order flop. Pat Cummins is generating some quality bounce from the wicket which has resulted in a certain level of discomfort to the openers, who are looking to rotate the strike at regular intervals. Howbeit, instead of talking directly to Rohit, Paine applied an intriguing technique of talking to Finch who was fielding at the forward short leg position.
The four-match series is poised at 1-1, after Australia won the second match in Perth. In an unexpected move, both the teams have announced their playing XI, with the visitors dropping the struggling duo of Lokesh Rahul and Murali Vijay, while the hosts have made only one change roping Mitchell Marsh in for Peter Handscomb.
Vihari took 25 balls and 33 minutes to score his first run as he batted with patience, which was lacking in previous opening partnerships in the first two Tests.