Pujara, who made 123 in the first innings, was twice given out to Nathan Lyon when on eight and 17, but survived two reviews to help India move into a commanding position on 151-3.
Lyon gave hope to most in a crowd of over 30,000 at the Adelaide Oval by removing India skipper Virat Kohli (34) late in the day for a crucial breakthrough.
India began their second innings with a slender 15-run lead after restricting Australia to 235 all out and extended their advantage despite the blow of losing Kohli, caught off an inside edge by Aaron Finch, in the 58th over.
Mitchell Starc was first to strike for Australia as opener Murali Vijay was caught by Peter Handscomb for 18 to leave India on 63-1 in the 19th over.
Fellow opener KL Rahul was removed by Josh Hazlewood, caught behind by skipper Tim Paine for 44, six overs later to leave India on 76-2 and a lead of 91. Pujara and Kohli then joined forces in a third-wicket stand of 71 to frustrate the hosts.
Kohli arrived at the crease to boos from one section of the crowd. He decided to forego his attacking style for a more measured approach as he made 34 from 104 balls. He was out pushing at a full ball from Lyon to Finch at forward short leg.
Earlier in the day, Australia had resumed on 191-7, 59 runs adrift of India’s first innings 250, with Travis Head unbeaten on 61.
Head had added 11 to his overnight score when he was caught behind off Mohammed Shami, who wrapped up Australia’s first innings by snaring Hazlewood in similar fashion next ball.
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