Tendulkar was batting on 71 and Kohli 50 as India ended the day at 182 for three in the first innings but still trail by 198 runs.
Australia, who resumed the day at 316 for seven, lasted just the first session before they were bowled out for 380 runs. Skipper Michael Clarke top scored with 130 while India off-spinner Ravichandran Ashwin returned with his career best seven for 103.
Chasing Australia's 380, openers Murali Vijay (10) and Virender Sehwag (2) departed by the middle of the sixth over, both being cleaned bowled by Pattinson (3/25). India were soon left struggling at 12 for two
Tendulkar, who has been struggling with form, then joined forces with Cheteshwar Pujara (44) and Kohli to bail out the Indian team with two crucial partnerships.
Tendulkar added 93-run with Pujara that brought back the innings on track and was then involved with Kohli in an unfinished 77-run partnership.
Tendulkar showed his class during the 128-ball stay hitting six fours. Tendulkar and Pujara attacked the Australian bowlers and didn't allow them to settle as India took tea at 84 for two after a dreadful start.
Pujara, who hit six fours in his 74-ball innings, became Pattinson's third victim and was clean bowled by a delivery that kept low and hit the middle-stump. Pattinson, however, was given just six overs despite being the most effective bowler.
Tendulkar and Kohli then scored rapidly as India added 98 runs in the last session. Kohli hit seven fours in his 84-ball unbeaten knock.
Tendular enroute to his 67th half-century also went past 7000 Test runs at home. Only Ricky Ponting, who has 7578 runs, is now ahead of Tendulkar.
In the morning session, Clarke's valiant 130 took Australia to a competitive total when lunch was called. Ashwin finished with career-best figures of 7-103 while left arm spinner Ravindra Jadeja finished with 2-71.
Resuming the day at 316/7, overnight batsmen Clarke and Peter Siddle (19) added 45-runs in the first hour as Australia went past the 350-run mark.
The partnership was going strong but Clarke in his attempt to go for the big shots tried to hit out Jadeja, didn't get to the pitch of the ball and holed out to Bhuvneshwar Kumar at long-off.
Siddle was back in the pavilion in the next over as Harbahajan Singh finally got a wicket in his 100th Test with Virender Sehwag taking a easy catch in the slips.
Pattinson added valuable 15 runs but Ashwin wrapped up the tail picking up Nathan Lyon (8), caught by Virat Kohli at backward short-leg.