India captain Virat Kohli said the 75-run win against Australia in the second test was the best under his captaincy, after his side fought back to level the four-match series at 1-1.

Under Kohli, who was appointed full-time test captain in 2015, India were unbeaten in 19 tests before they were thumped by 333 runs inside three days in the series opener against Australia in Pune.

India's hopes of squaring the series looked all but dead when they were dismissed for 189 in their first innings. But the world's top-ranked side fought back to keep Australia within reach and then batted resolutely to set a testing target.

Off-spinner Ravichandran Ashwin then picked up six wickets on the fourth day to lead India to a dramatic victory.

Kohli has scored just 40 in his four innings in the series and Australia off-spinner Nathan Lyon recently said their target is the "head of the snake", referring to India's batting mainstay.

"Till now, this is the best one definitely. It was a quite emotional game for us, quite draining as well," Kohli told reporters.

"Everyone got along together, we showed the team spirit, and a lot of people were talking about the head of the snake, but I think the snake did pretty well by itself, so it's not just about one individual.

"I'm pretty happy if they keep focussing on the head of the snake, and the snake can sting from a lot of directions. I think (this was) the sweetest victory for us."

The manner of the Pune defeat drew criticism for the world's top-ranked side, but Kohli said the team believed they will bounce back.

Australia have also played into India's hands by focussing too much on him, Kohli said.

"We said let their focus be on this, and if they don't focus on the others, they'll let the momentum slip, and that's exactly what happened," the 28-year-old said. "They basically played into our hands."

Kohli lauded the fifth-wicket stand of 118 in the second innings between Cheteshwar Pujara and Ajinkya Rahane that allowed the hosts to set Australia 188 for victory.

"In the last two years, it's one of the top two partnerships, or maybe number one, because retrieving the lost momentum and giving the team the lead was a question of character, and they both showed why they are India's best test batsmen," Kohli said.