At stumps on the third day, India were 213 for 4 in their second innings and had erased a first innings deficit of 87. The side is now looking good to post a fighting score for the visitors on a crumbling surface.
Australia had scored 276 in their first innings with left-arm spinner Ravindra Jadeja returning with best figures of 6 for 63 among the bowlers.
Pujara showed admirable temperament and was helped by flamboyant opener Lokesh Rahul's (51) second half-century of the match.
The unbroken 93-run fifth-wicket partnership between Pujara and Ajinkya Rahane (40 batting) could prove to be a defining one.
This was also the first time in the series that India managed to pull through a session without losing any wicket.
Pujara played 173 balls to hit six boundaries while Rahane also consumed 105 balls to hit three boundaries.
Lot of credit should be given to Rahul, who played both pacers and spinners well during his 85-ball knock that had four boundaries.
It took an absolute blinder from Australian skipper Steve Smith at first slip to remove Rahul, who also completed 1000 Test runs in his career.
Rahane, on his part, is playing one of the most crucial knocks of his career under pressure, displaying good technique and sound temperament needed in this scenario.
The duo had come to the crease when India were 120 for 4 with only a 33-run lead and six wickets in hand.
With three successive innings being a saga of middle and lower-order collapse, Pujara and Rahane showed a judicious blend of caution and aggression in their strokeplay.
Knowing fully well that defending on this track would be out of question, both the batsmen kept the scoreboard ticking with a fair amount of singles and doubles.
Importantly, both played the spin duo of Nathan Lyon (0/69 in 27 overs) and Steve O'Keefe (1/28 in 16 overs) well. Lyon again got turn and bounce but the strategy to wait for the off-break to turn helped them negate his threat.
For a change, they didn't play O'Keefe for the turn and that helped them negotiate the left-armer better.
For Australia, Josh Hazlewood (3/57 in 16 overs) was the pick of the bowlers. He cleaned up Abhinav Mukund (16) and Ravindra Jadeja (2), who was sent up the order to prop up the scoring.
Skipper Virat Kohli (15) was fell to a debatable DRS decision, where the ball kept low and the replays were inconclusive as to whether it grazed the base of his bat.
For India, a target of 200 plus is something that they would be initially looking for and a 250-run target could well prove to be a winning score on a fourth or fifth day track.
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