Test cricket’s highest run-scorer, who will be 40 on 24 April, has gone 31 innings without a Test hundred but revived his team after they were 12-2.
He shared an unbroken 77 with Virat Kohli, who reached 50 in the last over.
Earlier Australia resumed on 316-7 and were all out for 380, skipper Michael Clarke adding 27 to his overnight 103.
Clarke was reprieved on 128 when Cheteshwar Pujara spilled a difficult chance at mid-off but his 54-run rearguard with Peter Siddle ended four overs later when the captain advanced down the pitch to slow left-armer Ravi Jadeja, did not quite get to the pitch of the ball, and found long-off.
In the next over Harbhajan Singh celebrated his 100th Test by having Siddle caught at slip for 19 and Ravichandran Ashwin recorded his best Test figures of 7-88 when last man Nathan Lyon was smartly taken by Kohli to his right at backward short-leg.
The India spinner is playing his 13th Test but already boasts 70 wickets, claiming five or more in an innings six times.
It was raw pace that unsettled the Indian batsmen, in the form of James Pattinson, in only his eighth Test.
Generating impressive speed and hostility, he dismissed the openers in successive overs, Murali Vijay and Virender Sehwag both edging deliveries approaching 150 km/h onto their stumps.
There had been concerns in some quarters that Tendulkar’s considerable skills were on the wane, with no Test century since January 2011.
But he had no problems with 22-year-old Pattinson, calmly dispatching three of his first four balls to the boundary in classy fashion and the Victorian was replaced after a three-over spell.
Clarke chose not to call upon his strike bowler again until the fifth over after tea when he again was given a three-over burst.
Once again it was successful as Pujara, who had provided a useful foil for his legendary partner, was bowled on 44 by an off-cutter that appeared to keep a fraction low and rattled into the middle stump.
Kohli survived an anxious moment early in his innings when a ball from Siddle struck his thigh pad and trickled close to the stumps, but there were few other alarms for the Indian pair and a large crowd is expected today in the hope of seeing Tendulkar make his 52nd Test century.
