Rishabh Pant described his match-winning innings in India's stunning victory over Australia as "one of the biggest moments of my life".

Pant was unbeaten on 89 as India remarkably chased down 328 to beat Australia by three wickets at the Gabba, sealing a 2-1 series triumph as they retained the Border-Gavaskar Trophy.

It ended Australia's 31-match unbeaten run at the venue as the tourists pulled off one of the all-time great Test victories, leaving Pant thrilled.

"This is one of the biggest moments of my life now, and I'm happy that all the support staff and all my team-mates supported me even when I wasn't playing," he said during an on-field presentation.

"It's been a dream series. The team management always backs me and tells me, you are a match-winner and you have to go win the match for the team.

"I keep thinking every day that I want to win matches for India, and I did it today. It was a fifth-day pitch and the ball was turning a bit. I thought I have to be disciplined with my shot selection."

Ajinkya Rahane was almost lost for words to sum up his feelings, having come in as stand-in captain after Virat Kohli returned home to attend the birth of his child.

"It really means a lot to us. I don't know how to describe this victory. I'm just proud of all the boys, each and every individual," said Rahane, who contributed a brisk 24 from 22 balls in the final innings.

"We just wanted to give our best, not to think about the result. When I went in, conversation between me and [Cheteshwar] Pujara was Puji to bat normal and me to go for my shots, because we knew Rishabh and Mayank [Agarwal] were there.

"Credit to Pujara, the way he handled the pressure was magnificent, and Rishabh was brilliant in the end."

Having bowled India out for 36 to win the opening Test, Australia were left to rue a series that slipped from their grasp.

Captain Tim Paine conceded India deserved their success and urged his own team to look forward to the challenges ahead.

He said: "Absolutely disappointed.

"We came here to win the Test and win the series, it's been a bit of a trend that we were found wanting in the key moments and completely outplayed by a tough Indian side that fully deserves the win.

"I think there's lots of things we'll look back at, but what's done is done. We need to look forward now, there's a big series in South Africa coming up, we've been outplayed by the better side in this series."