Debutant Mayank Agarwal provided the base with a confident half-century before Kohli and Pujara steered India to a solid.
Make-shift opener Hanuma Vihari did not make many runs, getting just 8 off 68 balls in his 40-run stand with Agarwal but they batted out 18.5 overs.
At the other end, Pujara continued in his usual manner and brought up his 21st Test half-century off 152 balls.
Virat Kohli survived a hostile Mitchell Starc over towards the end to stay unbeaten on 47. Tim Paine grassed a caught behind chance of Kohli.
Pat Cummins continued to test the Indian batsmen with sharp bouncers at every opportunity possible. He took two wickets for hosts.
It was only the second instance in 11 overseas Tests this year that Virat Kohli was yet to arrive at the crease with 100-plus runs on the scoreboard.