Harbhajan Singh claimed four wickets and Amit Mishra picked up three as India completed a 172-run victory in the fourth Test to clinch the Border-Gavaskar trophy with a 2-0 series triumph in Nagpur.
Paceman Ishant Sharma struck two early blows in the morning session, getting rid of Simon Katich (16) and Michael Clarke (22), while leg-spinner Mishra, who had run out Ricky Ponting for eight in the morning, returned to pick up the wickets of Michael Hussey (19), Brad Haddin (four) and Jason Krejza (four) as India condemned the Baggy Greens to their first defeat since England's Ashes triumph in 2005.
Matthew Hayden struck a defiant 77, but was trapped lbw by his old rival Harbhajan, who also sent back Shane Watson (nine), Brett Lee (zero) and last man Mitchell Johnson (11).
The first and third Tests ended in draws, but with India winning the second Test in Mohali, the hosts only needed a draw here to clinch the series.
Victory, though, was the perfect parting gift for former skipper Sourav Ganguly, who had announced he would retire at the end of this Test.
Australia faced a stiff target at the start of play, needing 369 in three sessions.
Katich and Hayden resumed the chase in earnest and had looked to take the attack to India's bowlers in the morning.
India's new ball bowler Zaheer Khan, who conceded 13 runs in his first over yesterday evening, showed intensity and accuracy from the start, repeatedly beating Katich's edge in the first two overs.
Ishant was no less threatening but struggled to match Zaheer's consistency. Yet, he was the more successful as he snared Katich when the left-handed batsman looked to cart him through the leg side.
Katich only managed an edge which went high in the air towards gully and Mahendra Singh Dhoni ran round to take the catch.
Ponting was off the mark with an edged boundary through the slips and showed more authority when he drove Zaheer for his second four.
The Australia skipper then pushed a ball from Zaheer to Mishra at mid-on and set off for a single only for Mishra to catch him well short of the crease with a direct hit.
An unwell Clarke came to the crease with the support of a runner and Ishant immediately saw a confident appeal for lbw turned down by umpire Billy Bowden.
Clarke was almost caught and bowled by Ishant off the third delivery he faced and twice edged Zaheer in the next over for boundaries to third man, both edges flying just wide of VVS Laxman at second slip.
Clarke added 45 for the third wicket with Hayden when Ishant broke through, sending Clarke back to the pavilion when the batsman edged straight to Dhoni.
Hayden was dropped on 26 by Dhoni as he attempted to cut Harbhajan in his first over and again on 35 by Rahul Dravid at slip as he attempted a reverse sweep.
Hayden attacked with vigour immediately after lunch, bringing up his half-century with a boundary through mid-on off part-time off-spinner Virender Sehwag and bludgeoning consecutive boundaries off Harbhajan.
Together with Hussey, Hayden put on 68 runs for the fourth wicket to set India back slightly.
Harbhajan, however, persevered and reaped rich rewards as he trapped Hayden in front as the left-hander attempted to work a delivery on the on-side.
Mishra had by then ended the fourth wicket stand by sending back Hussey, turning it from the rough outside off-stump and inducing the edge which was held by Dravid.
Haddin's stay at the crease was brief and ended when he stepped down the track to cart Mishra over the top. He ended up hitting straight to Sachin Tendulkar who held his 100th catch in Test cricket.
Watson (nine) was Harbhajan's second wicket, snaffled by Dhoni as he attempted a cut shot and he had Lee caught by Murali Vijay at short leg as he lunged forward in defence.
Johnson was Harbhajan's final victim, given out leg before by umpire Aleem Dar to cue wild celebrations from the home contingent, who were joined by former captain Anil Kumble, who retired after the third Test.