Cheteshwar Pujara's unbeaten 82 saw the hosts comfortably chase down 155 for the loss of just four wickets after skittling their beleaguered opponents for 164 in their second innings.
Ravindra Jadeja took five for 58 to do most of the damage, with only tailender Peter Siddle offering any resistance with 50 - his second Test half-century - as Australia's batsmen undid all the good work achieved on Saturday and first thing on the third morning by Nathan Lyon.
The chase always looked well within India's grasp and was achieved with room to spare, despite two more wickets for Lyon, who finished with nine for the match. That was all after things had looked to be going Australia's way at the start of the day as India added only six runs to their overnight total.
A brilliant spell of spin bowling from Lyon had dragged Australia back into contention and the 25-year-old off-spinner did not take long to re-find his rhythm. Resuming on 266 for eight - having bowled out the tourists for 262 - the Indian tail had hardly settled before Lyon completed a career-best haul of seven for 94 by snaring the final two wickets with the first two balls of his first full over.
The renewed hope Australia may have harboured heading into the second innings with only a 10-run deficit swiftly diminished soon after they went out to bat again, however. Glenn Maxwell opened the batting in place of Ed Cowan, but perished in the fifth over to Jadeja, who then trapped David Warner in front for eight.
Phil Hughes (six) also succumbed to spin, coming forward to defend one from Ravichandran Ashwin and being undone by the turn. Shane Watson contributed five before having his middle stump dislodged by Pragyan Ojha, and the departure of Cowan (24) - batting at number three - lbw playing across the line to Jadeja next over left Australia reeling on 53 for five.
Steve Smith and Matthew Wade set about steadying the ship for the visitors and reached lunch on 89 for five. Neither man managed to get to 20, though. Smith was bowled between bat and pad by Jadeja, with Mitchell Johnson following for a duck with his very next ball.
Australia were now 94 for seven, but pace bowler Siddle proved an unlikely source of resistance. Ojha did for Wade on 19 and Ishant Sharma accounted for James Pattinson, but Siddle battled his way to a 45-ball 50 before he was stumped by Mahendra Singh Dhoni as he came down the track to Ashwin.
Australia needed their attack to fire to have any chance of rescuing the situation and, although Maxwell bowled Murali Vijay for 11, Pujara and Virat Kohli put India on the verge of victory. Kohli fell lbw to Lyon for 41 and the spinner also trapped Sachin Tendulkar for one, but Pujara continued to add runs at the other end and guided his side home.
- Sports & Recreation
- Peter Siddle
- Cheteshwar Pujara