India coach Ravi Shastri hailed his team's eight-wicket win over Australia on Tuesday as one of the great comebacks of all time, praising their character after a crushing loss in the first Test last week.

Despite missing superstar Virat Kohli, the Indians outplayed the hosts in Melbourne to silence their critics after being dismissed for 36 in Adelaide on their way to an eight-wicket defeat.

"I think this will go down in the annals of Indian cricket, world cricket, as one of the great comebacks in the history of the game," said Shastri after they levelled the series 1-1.

"To be rolled over for 36, then three days later to get up and be ready to punch was outstanding.

"I think the boys deserve all the credit for showing real character."

India's win was built on a first-innings century by stand-in captain Ajinkya Rahane on their way to 326 in reply to Australia's 195, with young debutant Shubman Gill also excelling with the bat.

But their bowling attack, minus Umesh Yadav who pulled out injured on Monday, also delivered, with a standout performance from Mohammed Siraj, another on debut.

Shastri said both Siraj and Gill had big futures ahead.

"These two debutants showed a maturity and flair and discipline and it was great to see," he said.

"Today Siraj, his effort was outstanding. He might not have the numbers to show for it, but the discipline and the ability to bowl long spells was outstanding.

"More than anything, they have shown great character."

Kohli, watching at home in India ahead of his wife giving birth to their first child, was equally impressed by what he saw.

"What a win this is, absolutely amazing effort by the whole team," he tweeted.

"Couldn't be happier for the boys and specially Jinks [Rahane] who led the team to victory amazingly."

Shastri paid particular tribute to Rahane, who in contrast to Kohli is a less flamboyant captain, but equally effective.