Requiring 133 to win on the final day, India survived a slight stutter in the end to reach the target with 15 balls to spare.
Day 4 summary: Australia were 75 for 3 in their second innings and trailed India by 16 runs at stumps on day four. The visitors lost David Warner, Ed Cowan and Steven Smith during the 21 overs of their innings. Swing bowler Bhuvneshwar Kumar picked all three wickets to fall.
India made 499 in response to Australia's 408.