Published: 2018-12-31 06:25:56 BdST
India, denied victory on day four by the tail-end resistance of Pat Cummins, were forced to wait nearly two-and-a-half hours for play to begin due to rain at the Melbourne Cricket Ground but when the weather cleared their bowlers wrapped up Australia's innings for 261 in 22 minutes.
In his second over, seamer Jasprit Bumrah had Cummins edge to Cheteshwar Pujara, who took a sharp, low catch in the slips to remove the bowler for a personal high score of 63.
Paceman Ishant Sharma then sealed the result when he had Nathan Lyon edge behind to wicketkeeper Rishabh Pant for seven when attempting to slog the ball.
The wicket triggered bear hugs and backslaps among the Indian players as travelling fans in the sparse crowd roared with joy.
Having dominated with bat and ball throughout the one-sided Boxing Day clash, Virat Kohli's men will head to the Sydney Cricket Ground with a genuine belief they can become the first Indian team to win a series Down Under.
The win also saw them retain the Border-Gavaskar Trophy contested between the nations after claiming last year's series 2-1 at home.
"We’re not going to stop here, this has only given us more confidence to go out in Sydney and play even more positive cricket," Kohli said at the trophy presentation.
"The job is not done yet ... We want to win the last Test as well.
"It’s all about taking pride in the roles we were given and executing them."
Resuming on 258 for eight, 141 runs short of victory, Australia's best hope was for rain to wash out the final day but the morning showers merely delayed the inevitable.
They had been set a daunting victory target of 399 shortly before lunch on day four, and crumbled after India's pacemen attacked the stumps with cold-blooded assurance.
The pride of Cummins and Lyon allowed Australia to limp into day five but the match had slipped away from the hosts on the morning of day three, the rampaging Bumrah taking 6-33 to rout Paine's side for 151 and carve out a first-innings lead of 292.
Bumrah claimed 3-53 in the second innings for a match haul of 9-86, and was deservedly named man of the match.
The recalled Ravindra Jadeja enjoyed a successful return, claiming five wickets for the match with his wily left-arm spin.
Barring Cummins' heroics -- the fast bowler claiming nine wickets for the match and career-best figures of 6-27 in India's second innings -- there were few positives for Tim Paine's Australia.
The hosts will head into the final match pondering a litany of problems and whether their victory in the second Test in Perth was a false dawn rather than a turning point for a depleted team playing without their two top batsmen in former skipper Steve Smith and his vice captain David Warner.
The pair have three months left on their bans for their part in the Cape Town ball-tampering scandal but Australia will be eager to reinstate them as soon as possible.
"It’s a bit disappointing, no doubt," Paine said.
"We felt we made some strides in Perth but with an inexperienced batting lineup at times you’re going to have performances like we did in the first innings.
"So we’ve got to learn from that, and get better really quickly before we go to Sydney."