Warner chipped away patiently to reach his 50 off 105 balls, his second Test half-century against India and sixth overall.
Warner and Cowan stood firm at the crease before the first break, driving Australia to the first century opening stand by either side so far in this series.
At lunch, Australia was 0-109 with Warner on 54 and Cowan closing in on his half-century, on 43.
Cowan was fortunate on 35 when his attempted cut shot whizzed past Virat Kohli at slip who was unable to get his left hand on the delivery bowled by left-arm spinner Pragyan Ojha.
Warner on 50 also squirted an edge past Kohli's right hand from the bowling of left-arm spinner Ravindra Jadeja.
Australian captain Michael Clarke won the toss and elected to bat, in third of the four-Test series which started a half-hour earlier than scheduled to make up for a washed-out and abandoned day one.
The weather, though, was looking much better on the morning of day two, with sunny skies and no rain in sight.
Clarke leads a patched-up team which includes veteran wicketkeeper Brad Haddin, who will play for Australia for the first time since losing his place to the younger Matthew Wade, who was ruled out after suffering an ankle sprain during a training session.
The Aussies dramatically dropped vice-captain Shane Watson and paceman James Pattinson for the match, replacing the pair with all-rounder Steve Smith and youngster Mitchell Starc.
Spinner Nathan Lyon was called up at the expense of Glenn Maxwell.
The Indians dropped spinner Harbhajan Singh for the Mohali clash, replacing him with Pragyan Ojha.
The Indians lead the series 2-0 with two matches to be played.
INDIA XI: MS Dhoni (capt), Murali Vijay, Shikhar Dhawan, Cheteshwar Pujara, Sachin Tendulkar, Virat Kohli, Ravindra Jadeja, Ravi Ashwin, Pragyan Ojha, Bhuvneshwar Kumar, Ishant Sharma.
AUSTRALIA XI: Michael Clarke (capt), David Warner, Ed Cowan, Phil Hughes, Steve Smith, Brad Haddin, Moises Henriques, Peter Siddle, Mitchell Starc, Nathan Lyon, Xavier Doherty.