India captain Rohit Sharma and his Australia counterpart Steve Smith agreed the fate of the four-test series for the Border-Gavaskar Trophy was sealed in Delhi where the resilient hosts bounced triumphed by six wickets inside three days.
India comprehensively won the series opener in Nagpur but were under pressure in the low-scoring contest in Delhi where Australia posted 263 and reduced the hosts to 139-7.
Axar Patel led a spectacular rearguard action to help India post 262 and Australia imploded in their second innings when they were shot out for 113 with Ravindra Jadeja leading their rout with 7-42.
"We knew how important it was to start the series well but the Delhi test match is something I'm really proud of," Rohit said after India won the four-test series 2-1 as the final match ended in a draw in Ahmedabad.
"We were very much behind the game and to come back from the situation that we did shows a lot of character and the fight that the boys have in them."
While India retained the trophy with back-to-back wins in Nagpur and Delhi, Australia found themselves buffeted by a series of injuries.
Quick Mitchell Starc and allrounder Cameron Green missed the first two tests with finger injuries, while paceman Josh Hazlewood returned home without playing a match.
They crisis was further compounded in Delhi where opener David Warner fractured his elbow and returned home ending a poor series.
Regular skipper Pat Cummins also flew home after the second test to be with his ailing mother who passed away last week leaving Smith in charge of a battered squad.
Australia bounced back in Indore where they beat India inside three days but had to settle for a draw on a flat batting track at the Narendra Modi Stadium where only 22 wickets fell in five days.
Smith felt the outcome of the series could have been different had they grabbed their opportunity in Delhi.
"That hour of madness, I suppose, in Delhi really cost us in that game," Smith said at the presentation ceremony.
"But I think coming back from that in the next game in Indore, we fought back really nicely, and in this game as well we put it all together.
"Unfortunately the wicket was probably a little bit too flat for a result in the end, but it was good cricket all the same."
The teams will now clash in a three-match one-day series beginning in Mumbai on Friday.