Cowan and Warner both batted Australia into a strong position with their 139-run opening stand with Warner ending up making 71 and Cowan eventually falling for 86, but their teammates have failed to back them up aside from an unbeaten 58 from Steve Smith.
Smith has looked the best of all Australian batsmen against the spin of Ravi Ashwin, Pragyan Ojha and Ravindra Jadeja as he remains 58 not out at stumps in his first Test for Australia since the Sydney Ashes Test of January 2011.
However, Australia went from looking solid at 4-244 with Smith and Brad Haddin going well, to losing 3-7 to now be 7-273 at stumps with Mitchell Starc joining Smith and remaining not out on 20.
After the entire first day was washed out due to rain giving the Australian team even longer to stew on the dramatic build-up having already lost the first two Test matches, Cowan and Warner made a tremendous start.
Captain Michael Clarke started the day well for Australia when he won the toss and elected to bat first.
Cowan and Warner survived unscathed right throughout the morning session with the score 0-109 at lunch and then after the interval, the pair continued on their merry way both going beyond 50.
Things were going along smoothly at 0-139 before in the 48th over of the innings, left-arm spinner Jadeja turned Australia's innings.
He firstly picked up the wicket of Warner for 71 when he had him edging the ball onto his pad and then it ballooned up for Indian captain and wicket-keeper MS Dhoni to comfortably take the catch.
That brought to an end the opening stand of 139 with Warner's 71 including nine boundaries.
Clarke then strode to the crease after he moved himself up the batting order to No. 3 but it did not pay dividends as he was out stumped first ball also off Jadeja.
Phil Hughes did not look any more comfortable coming into bat at No. 4 and continued his disastrous run against spin bowlers in India.
He looked all at sea especially facing Jadeja and Ojha, who came in to replace Harbhajan Singh, and eventually it was Ojha who had him caught behind by Dhoni for two off a painful 31 deliveries.
Australia was then 3-151, but since then Cowan was joined by Smith and the pair guided the visitors safely to tea.
Cowan was living dangerously after the break and offered a life that wasn’t taken by the Indians, but they didn’t need a second chance and eventually Cowan was out for 86 when caught Virat Kohli off the off-spin bowling of Ashwin.
Cowan's 86 came off 238 balls and included four boundaries.
Haddin then made his intentions clear from the outside hitting Ashwin for a six immediately but when Ishant Sharma came back on, he had no answer and was bowled for 21.
Moises Henriques then suffered the same fate without scoring second ball and then Peter Siddle failed to score from 14 deliveries before being adjudged leg before off Jadeja.
Australia was then 7-251 and now Smith and Starc have survived through until stumps.
Jadeja has 3-56 for India with Sharma taking 2-41, Ojha 1-62 and Ashwin 1-64.