Dom Bess took four wickets as England survived Rishabh Pant's counter-attack to end day three of the first Test in Chennai 321 runs ahead of India in an entertaining contest.

England were bowled out for 578 and India, after initially toiling, closed 257-6 thanks to a sparkling knock from Pant at M. A. Chidambaram Stadium.

Bess snared home skipper Virat Kohli for 11 and vice-captain Ajinkya Rahane for one, before putting an end to Pant and Cheteshwar Pujara's rearguard, leaving England in a strong position to take the lead in the four-Test series.

The tourists added a further 23 runs for their final two wickets in the opening hour of Sunday's session, with Bess (34) falling lbw to Jasprit Bumrah and James Anderson missing a sweep against Ravichandran Ashwin for a single run.

India's task of chasing down England's tally was made all the more difficult when reduced to 154-4 at tea, including the loss of Kohli for just 11 when caught at short-leg by the bowling of Bess.

Kohli's dismissal came after Rohit Sharma was sent packing by Jofra Archer for six and Shubman Gill (29) was undone by Anderson's diving catch after averaging a run-a-ball up to that point.

Bess rammed home England's advantage by taking Rahane, who went to a superb Joe Root catch after chipping a drive to short cover, but India - 73-4 at that point - finally steadied the ship through Pujara and Pant.

Pujara racked up 11 fours from 143 balls en route to 73, though it was Pant who helped make a more telling dent in England's tally with nine fours and five sixes as he targeted the spin of Jack Leach.

However, Bess returned and took both Pujara and Pant, the latter being caught at deep extra by Leach for 91 from 88 balls.

Ashwin and Washington Sundar frustrated England late in the day, ending the session on eight and 33 not out respectively.

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."

Tim Paine admitted he let Australia's bowlers down with three dropped catches as India ground out an unlikely draw in the third Test at the SCG.

India resumed day five on 98-2 with a victory target of 407 and they appeared to be sliding towards defeat when Nathan Lyon dismissed captain Ajinkya Rahane for four.

However, Rishabh Pant gave the tourists hope of pulling off the upset with a phenomenal knock despite dealing with an elbow injury, benefiting from being put down by Paine off Lyon on three and 56.

Lyon removed Pant three runs shy of his century and after Cheteshwar Pujara (77) fell to Josh Hazlewood, heroic defence from Hanuma Vihari (23 off 161 balls) and Ravichandran Ashwin (39 off 128) after the former tweaked his hamstring saw India over the line.

Paine also spilled Vihari on 15 late in the final session when he dived to his right, with India sitting at 334-5 at stumps to keep the series level at 1-1 ahead of the fourth Test at the Gabba, which begins on Friday.

"I'm bitterly disappointed, I pride myself on my wicketkeeping," said Australia captain Paine.

"I haven't had too many worse days than that today, it's a horrible feeling knowing our fast bowlers and our spinner bowled their hearts out and gave everything to the team.

"I certainly feel I let them down. I have to wear that, but I'll get another crack at it next week so move on.

"We created enough chances to win. I wouldn't say it's deflating, I thought there was a lot of positives out of the game and it was an awesome game of Test cricket.

"India fought bloody hard like we knew they would, clearly we are disappointed not to get a win but thought there were some good signs for us after the Melbourne Test."

Rahane praised Pant for boosting India on a daunting final day and the India skipper is confident the wicketkeeper-batsman will be fit for the fourth Test.

"Yeah, credit to him [Pant]. I mean, we made the strategy, but in the end it's all about that player showing the character," Rahane said.

"It was all about a left-hand-right-hand combination in the middle that worked out really well for us. Credit to him, the way he batted, attacking innings, backed himself really well.

"Rishabh is all right. Injuries, I think, we cannot control. We are just focusing on the Brisbane Test match. [Ravindra] Jadeja, the physios are going to take the call, but apart from that, we have to see how Vihari is feeling. Looking forward to Brisbane now."

India held firm to deny Australia and secure an incredible draw in the third Test in Sydney on Monday.

Australia looked in position to take a 2-1 series lead, needing eight wickets on the final day at the SCG, but were left frustrated by a stubborn India batting line-up and costly dropped catches.

Rishabh Pant (97), Cheteshwar Pujara (77), Hanuma Vihari (23 off 161 balls) and Ravichandran Ashwin (39 off 128 balls) helped ensure India were level heading into the final Test in Brisbane starting on Friday.

The SCG pitch played few tricks on day five, and Pant even had India dreaming of an amazing win, the tourists eventually finishing at 334-5, 73 runs adrift of a victory they stopped chasing after Vihari hurt his hamstring.

Josh Hazlewood (2-39) and Nathan Lyon (2-114) made breakthroughs, but Australia were unable to do enough in a Test they looked destined to win as Tim Paine dropped three catches.

Australia landed an early blow as Lyon had Ajinkya Rahane (4) caught at short leg by Matthew Wade.

But Pant – who suffered an elbow injury on Saturday – was put down twice by Paine, on three and 56, off Lyon, and he counter-attacked superbly to put the pressure on the off-spinner.

Pujara brought up 6,000 Test runs, the 11th Indian to achieve the feat as he continued to frustrate Australia.

Pant looked capable of leading India to a shock victory before falling just short of a third Test century, caught by Pat Cummins at gully after trying to attack Lyon again.

The second new ball brought a key wicket for Australia as Hazlewood produced a wonderful delivery to bowl Pujara.

A pair of reviews were unable to get Ashwin, who was dropped on 15, a diving Sean Abbott – on for the injured Will Pucovski (shoulder) – unable to hold onto a tough chance.

Vihari and Ashwin, showing no intent to score, remained stoic and defended well against an increasingly desperate Australia.

Paine dropped another chance after Vihari edged a Mitchell Starc (0-66) delivery and it proved to be the final opportunity as India held on for a draw.