Skipper Rohit Sharma was unbeaten on an assured 85 as India turned the screw on Australia despite debutant spinner Todd Murphy claiming his third wicket of the opening Test on Friday.
India took lunch on day two at 151-3, closing on Australia's first-innings 177, on a Nagpur pitch which is expected to turn more as the match progresses.
Murphy, an off-spinner who claimed KL Rahul as his first Test wicket on Thursday, trapped Ashwin lbw -- a decision successfully reviewed by Australia -- and got Pujara caught at short fine leg.
Rohit started cautiously on his overnight 56 before he smacked fast bowler captain Pat Cummins for six over deep-square leg and hit another over the fence from spinner Nathan Lyon.
He mixed the right dose of caution and aggression and despite losing Ashwin and Pujara stood firm to see off the first session, as India trail by 26 runs.
Spinner Ravindra Jadeja was the first-day hero with his 5-47 against the tourists, who elected to bat first at the start of the four-match series, but were all out shortly after tea.
Images showed Jadeja rubbing a mystery substance on his finger, raising the possibility of ball tampering.