Smith (80*) was in the middle alongside comeback man Glenn Maxwell (19*) in a session where Australia scored 85 runs in 30 overs at the loss of Peter Handscomb (19).
It was a less productive session for the hosts, who had taken three crucial wickets in the first two hours of play, reducing the visitors to 109 for three.
Ajinkya Rahane was the stand-in captain in the middle as Virat Kohli missed majority of the second session after hurting his shoulder with an awkward dive in the morning.
Such was the impact that he had difficulty in standing up and was seen grimacing in pain, clutching his right shoulder to be rushed out of the field immediately.
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However, it was a memorable outing for rival skipper Smith, who became the third fastest batsman in terms of matches played to complete 5000 Test runs in his 53rd Test. Sir Don Bradman had reached the milestone in his 36th Test, while Sunil Gavaskar took 52 matches to get past 5000.
Umesh looked the most impressive Indian bowler and gave the the only breakthrough of the session when he trapped Handscomb LBW with a brilliant inswinging yorker.
After Handscomb's departure, Smith found a fine ally in Maxwell.
Earlier, Smith won a fine toss as their openers Matt Renshaw and David Warner played with a positive intent and cruised to 50 for no loss in 9.3 overs.
But after spin was introduced at both ends in the 10th over, Ravindra Jadeja (1/49) struck in his first over with Warner (19) offering a simple return catch to the left-arm spinner.
Seventh over and Ashwin came in with his 'bunny' Warner at the opposite end.
At the other end, Warner took his time and hit his first boundary after 22 balls with an elegant cover drive off Yadav.
With Warner looking to break free, Kohli employed spin attack at both ends and Jadeja was welcomed by the Aussie vice-captain with another crunching drive.
REOPENS DEL 24
In the middle of a fine run, 20-year-old Renshaw looked to complete a third half-century in as many Tests, before falling six runs short.
Ashwin too opened his account after India brilliantly used the DRS to dismiss Shaun Marsh (2) as India struck twice before lunch.
India made one change in the playing eleven, bringing back a fit-again Murali Vijay in place of Abhinav Mukund.
The Aussie made the two forced changes with Glenn Maxwell and Pat Cummins figuring in XI in place of the injured Mitch Marsh and Mitchell Starc.
The series is locked 1-1 with the last match in Dharmasala from March 25-29.