India's pace attack, led by Mohammed Siraj in his third test, performed admirably despite dealing with yet another injury.
Rohit was elegant as ever in his 44 off 74 balls before Nathan Lyon in his 100th Test enticed him to come down the track but the half-chip-half-loft was safely pouched by Mitchell Starc in the deep.
India's reply began shakily after lunch, with the relentless Pat Cummins having opener Shubman Gill caught in the slips for seven.
Indian skipper Ajinkya Rahane at two will resume the game on Sunday at Gabba for the visiting team who are 62 for two, lagging behind 307 runs of Australia 369 in first innings.
Marnus Labuschagne had struck a century on the opening day for Australia.
Washington, at the other end and on his Test debut, provided able support as he kept rotating the strike to keep the scoreboard ticking. At the tea break, India's score read 253/6.
It was very similar to his dismissal off Moeen Ali at the stroke of tea during the 2014 series and that was also after being set in the middle-order.
The tourists only need to draw the Test to retain the Border-Gavaskar Trophy, two years after their breakthrough 2-1 series win in Australia in 2018/19.
India went on to add 99 runs in the session.
Pacer Shardul Thakur (3/94) and debutant off-spinner Washington Sundar (3/89) shared four of the five wickets that fell today.
For an attack as thin on experience as India, the effort in adverse times can only be commended.
Rohit Sharma bowled his remaining over.
Thakur got his second victim of the day in his next over, Cummins falling lbw for two as the Australians fell to 315-8.
The off-spinner then snared the key scalp of Rohit Sharma, who had looked increasingly risky prior to giving Mitchell Starc some catching practice in the deep while on 44, as India reached 62-2 at tea.
Playing his 100th Test, Lyon soaked up the acclaim of the home crowd, pushing Australia past 350 before he was bowled by Sundar for 24 off 22 balls.