At the Adelaide Oval, Pujara scored 73 runs (135 balls, 9 fours) and put on 81 runs with skipper Virat Kohli (48 not out, 85 balls, 6 fours) in the post-lunch session as they continued to reduce the hosts' advantage.
Australia had declared at 517/7 in their first innings.
The session had begun with Pujara and Kohli under some duress from the Australian pacemen before lunch. But they soon found their rhythm to settle down on a pitch that is still quite helpful to bat on.
The two batsmen had scored runs quickly and their 50-run stand for the third wicket came up in the 39th over off only 54 deliveries. It seemed India were pivoting well in this crucial session of the Test and setting themselves up for a strong score in reply to the Australian total.
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But then Nathan Lyon (1-63), who had been hit out of the attack by Murali Vijay (53) before lunch, returned and bowled a brilliant probing spell to the two set batsmen.
It ended with Pujara being bowled in the 50th over of the innings as he defended the ball but left enough gap for it to break the stumps.
It brought Ajinkya Rahane (19) to the crease and he was still there at the tea-break, somehow surviving a probing spell by Mitchell Johnson (1-68) towards the end of the session.
Earlier, Vijay struck his seventh Test fifty to steady India in the morning session. He put on 81 runs with Pujara for the second wicket after Australia had declared at their overnight score.