Kohli's entrance was met by a huge roar but his innings did not last long as he was caught by a spectacular one-handed take from Usman Khawaja off a Cummins delivery for just three.
India will resume at 9-250, having crashed to to 3-19 then 6-127 before Pujara rallied with help from the tail.
Australian bowling coach David Saker said it was a premeditated plan for the quicks to pitch it up and lure India's batsmen into false shots.
Kohli's side had slumped to 86 for five after lunch, falling to a combination of awful shot-making and fierce Australian pace after winning the toss.More news: New satellite images reveal North Korea is expanding key missile base
The ball screamed toward the slips cordon, where a leaping Khawaja took a leaping one-hander that will take some beating for catch of the summer. It was a very poor show from India with the bat - all except for Pujara, Rohit Sharma and Ravi Ashwin.
Without the Indian talisman, Pujara anchored vital partnerships with young wicket keeper Rishabh Pant and Ravichandran Ashwin before completing his 16th test century with a flick off his pads after scoring his 5,000th run in tests.
The 28-year-old pacer, however, said it is still early stage and they will need to work hard to achieve a win.More news: Russian HIV Patients Deal With Persistent Stigma As Incidence Rises
"It was a good little momentum-goer too, because we got a couple of early ones. and we got a few more so it was nice".
Cummins got airborne and - off balance and with one stump to aim at - unleashed a direct hit that left Pujara well short of his ground. He also credited skipper Tim Paine for attacking the Indian batsmen right through the day.More news: China and HK shares slump, tech leads losses after Huawei CFO arrest
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