Australia now have a 39-run lead after India declared their innings at 247 for 9 in the first hour of the second day, with skipper Ajinkya Rahane remaining unbeaten on 117.
With India and Australia playing the second T20I on the same day, the visiting Test squad has been named India 'A' for the first of the two practice games
Chasing a stiff target of 195, Chakravarthy (5/20) and Pat Cummins (3/17) gave the Delhi Capitals batsmen a torrid time to restrict them to 135 for 9 in 20 overs