Needing 155 to win at Feroz Shah Kotla, Cheteshwar Pujara led the Indian chase with an unbeaten 82 in the final session on day three.
Live updates from day three of the fourth and final Test between India and Australia at the Feroz Shah Kotla on Sunday.
Day 2 summary: India were 266 for 8, four runs ahead of Australia's first innings total, at stumps on day two.
Bhuvneshwar Kumar was batting on 10 as the day ended with the dismissal of Ravichandran Ashwin, who made 12. Murali Vijay and Cheteshwar Pujara made 57 and 52. Nathan Lyon took five wickets for Australia.