Aussies put an end to 35 years of hurt.

Australia wrapped up their first series win in India in 35 years after an overwhelming victory by 342 runs in the third Test in Nagpur.

The tourists declared their second innings on 329 for five to set India a mammoth target of 543 runs to win but they were never in the hunt for saving the match and Australia bowled them out for 200 to claim a crushing win with more than a day to spare.

Pacemen Jason Gillespie and Michael Kasprowicz wasted no time in tearing through India's top order in the second innings.

Despite a spirited 52-run final-wicket stand between Zaheer Khan and Ajit Agarkar, Damien Martyn produced an outstanding catch to dismiss Khan off the bowling of Shane Warne to secure Australia's first series win in India since Bill Lawry's team came home victorious in 1969.

It was a happy end for Martyn, who earlier in the day, had missed out on his second century of the match when he was dismissed for 97.

Resuming on 202 for three, Michael Clarke and Martyn had taken the score to 319 before Anil Kumble claimed his first wicket of the innings.

Clarke smashed the spinner to midwicket but was brilliantly caught by Mohammad Kaif for 73.

Skipper Adam Gilchrist joined Martyn, who was three short of a ton when he edged Zaheer Khan to wicketkeeper Parthiv Patel and the Australians immediately declared.

Aakash fell to Gillespie to give India the worst possible start at one for one and the same bowler claimed his second victim two overs later, clean bowling Rahul Dravid for two.

Sachin Tendulkar (two) scooped a Glenn McGrath ball to gully, where Martyn clung on for the catch, VVS Laxman hooked Mike Kasprowicz straight to McGrath at fine leg and Mohammad Kaif was caught behind off Kasprowicz by Gilchrist for seven as India crumbled under the pressure.

Virender Sehwag (58) and Parthiv Patel (32) provided some resistance but they could not halt the Australian charge as Anil Kumble (two) was clean bowled by Gillespie, who finished with four for 22.

Murali Kartik (22) was then harshly adjudged caught behind off McGrath and although Khan and Agarkar produced a superb late flurry of boundaries it was too little too late for India.

Australia skipper Gilchrist was almost at a loss for words after seeing his team secure the series.

"It's just a magic feeling really," he said. "It's a wonderful occasion to share with a great bunch of people, and it's an emotional time.

"I think our batting has won us the series, but our bowlers gave us the best chance of winning -( they were fantastic."