Rahul (96 off 185 balls) and Pujara (55 off 122) held the innings together before the touring Australians fought back on day when 77.1 overs were bowled due to rain towards the end of day's play.
Young Shreyas Iyer was another batsman who contributed 39 off 58 balls.
Andrew Fekete and Steve O' Keefe took wickets each for the visitors.
The Karnataka batsman played well but missed out on a century by giving a simple catch at mid-on to Usman Khawaja off pacer Sean Abbott. His gritty knock saw him hit 14 boundaries besides sharing a crucial 107-run stand with skipper Pujara.
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Pujara, who is leading the A side after being overlooked from the playing eleven in the one-off Test in Bangladesh last month, spent substantial time at the crease, collecting seven fours in the process.
Feteke, who claimed 2 for 38 in 17 overs, later said the wicket was slow, helping him get rid of Pujara.
"Due to slowness of the wicket it is difficult to score runs," he said.
India lost opener Abhinav Mukund cheaply before Rahul and Pujara steadied the innings.
The quick fall of Pujara and Karun Nair (0) put the hosts in a spot of bother but Rahul and Iyer stemmed the fall of wickets and at tea, India were 175 for 3 in 57 overs.