The experienced Pujara faced 246 balls in his gutsy knock - passing 5 000 test runs for his 16th test century - as the wickets tumbled around him, including superstar captain Virat Kohli for three.
But Kohli's wicket, looking to drive a Cummins delivery which pitched full and outside off stump, was symptomatic of a wider tendency by India's batsmen to play at deliveries they would have been better off leaving alone.
India finished the day on a respectable 9-250 after it looked like they may have been skittled for a sub-par score.
"Pujara was like a sage on this first day".
Cummins provided the breakthrough of Ashwin just before the new ball.
Australia's bowlers will pay the price for their batsmen's sins after being boldly sent into an Adelaide heat wave without a safety net against India.
"Lyon understands the pace of the wicket, the bounce that it's going to provide him, and where the fielders should be, " Kohli said.
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"It was hot but I was set and I knew I could play my shots". Runs were hard to come by for Australia with quick Jasprit Bumrah bowling five consecutive maidens during the middle of the session. "We got it wrong in the end and let it slip a bit but for the most part we were exceptional".
"The odd ball is skidding on and the odd ball is holding a bit more.it's kind of two-paced".
After winning the toss, India rued reckless batting from their top-order starting with openers K.L. Rahul and Murali Vijay falling to loose drives.
When superstar Virat Kohli fell to an unbelievable Usman Khawaja catch at gully for three, India were reeling at 3-19. He has to paper over the cracks left by the bans on Steve Smith, David Warner and Cameron Bancroft and also win the trust of an Australian audience still aghast over the ball-tampering controversy.
Ajinkya Rahane (13) fell in the slips to an impulsive stroke as India crashed to 56-4 at lunch.
Indian players celebrate after Australia's Shaun Marsh was dismissed during the first cricket test between Australia and India in Adelaide, Australia, Friday, Dec. 7, 2018.
In day-night Tests in the past three years, Adelaide's opening-day crowds numbered around 47,000, 32,000 and 55,000. The Saurashtra right-hander has given the blueprint for the rest of the batsmen to follow after another poor show by the top order after Virat Kohli won the toss and chose to bat.