India had resumed on 166 for six in their second innings chasing an improbable 500 runs for victory but their tail-end batsman lasted just 58 minutes on a hot and sunny fifth morning of the match.
Australian paceman Peter Siddle, who took 5-49 in India's first innings, was named Man-of-the-Match, while the Man-of-the-Series was his captain Michael Clarke, who hit triple and double centuries in the series.
"I think the job we've done over the last month has been outstanding. It hasn't been easy despite the 4-0, we've had to work our backsides off," Clarke said.
"We certainly should be proud of what we've done." The end came when spinner Nathan Lyon (4-63) dismissed Umesh Yadav caught behind for one, condemning India to a humiliating eighth successive overseas Test defeat after last year's 4-0 whitewash in England.
The series defeat in England saw India relinquish the top spot in the Test world rankings but they had still arrived Down Under confident they could claim a first series triumph in Australia.
It was not even close as Australia won the first Test in Melbourne by 122 runs and followed that with an innings and 68-run win in Sydney and an innings and 37-run triumph in Perth.
With world class batsmen like Rahul Dravid, Sachin Tendulkar and VVS Laxman all having failed to fire yet again on Friday, there was little hope of India rescuing a draw by batting through the final day at the Adelaide Oval.
Nighwatchman Ishant Sharma (2) was the first to go in the third over of the morning when he got a nick to a delivery from quick Ryan Harris and was caught behind without any addition to the overnight score.
Wriddhiman Saha, standing in as wicketkeeper for banned India skipper Mahendra Singh Dhoni, was dismissed in the next over in similar style for three.
Zaheer Khan hit a typically bullish 15 off 18 balls before swinging at a short Ben Hilfenhaus delivery and getting a thick edge to David Warner at short cover, leaving Yadav and Ravi Ashwin (15 not out) as the final partnership.
"I think Australia played brilliantly throughout the series and stepped up when it was needed," said Dhoni, who missed the match because of India's slow over rate in Perth.
