On the final ball of the day, as he tried to sneak a quick single, Cummins' throw at the stumps sent him back to the pavilion after a gritty knock of 123 runs.
Pujara's resolute stay helps India cross the 250-run mark, which will be a morale booster for their bowling unit when it's their turn to ply their trade with the Kookaburra.
They lost wickets at regular intervals as the hosts' bowlers got them on the mat. It was a very poor show from India with the bat - all except for Pujara, Rohit Sharma and Ravi Ashwin.
Aussie pacers made ideal use of the new ball to get rid of KL Rahul, Murali Vijay and Virat Kohli inside the first 11 overs with Mitchell Starc, Josh Hazlewood and Pat Cummins striking once each. "As a captain, it will be an opportunity to leave a legacy and be the first Indian team to beat Australia in Australia".
"We got the wickets the way we thought we might get the wickets", he told the Seven Network.More news: Pregnant Duchess Meghan Markle's Growing Baby Bump Visible During Christmas Carol Event
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Veteran Murali Vijay, in the side after young gun Prithvi Shaw suffered ankle ligament damage in a warm-up game, didn't last much longer, caught behind by skipper Tim Paine off Starc for 11.
In marched Kohli to a huge roar from the crowd, but Usman Khawaja at gully spectacularly caught him off a Cummins delivery as he attempted a drive, out after facing only 16 balls.
It will take some grab to top Khawaja for the catch of the summer.
Vice captain Ajinkya Rahane and Pujara worked to steady the ship. Rahane miscued yet another drive, this time to Handscomb at second slip. They slid further when Rohit Sharma holed out attempting a slog off Lyon. Nevertheless, he played one shot too many and was dismissed by off-spinner Nathan Lyon, caught by Marcus Harris at the deep square leg region.
Pujara then enjoyed 41-run and 62-run partnerships with Pant and Ashwin respectively before the 30-year-old, playing his 65th Test, was run out by Cummins, who along with Hazlewood and Starc each picked up two wickets.