On a Feroze Shah Kotla track which is not conducive for good batting, India chased down a tricky target of 155, largely due to Cheteshwar Pujara's dazzling strokeplay as the home team recorded their biggest ever series win in the 81-year history inside three days.
Pujara, who was battling pain as he was playing with a swollen hand, enthralled one and all with his perfect technique on a rank turner, scoring a brilliant unbeaten 82 off 92 balls with 11 boundaries.
For Australia, it was the first time in 43 years to suffer a 0-4 series whitewash after Bill Lawry's side did the same in South Africa in 1969-70.
There were a few jitters when India lost Virat Kohli (41), Sachin Tendulkar (1)and Ajinkya Rahane (1) in quick succession but Pujara kept his cool in company of skipper Mahendra Singh Dhoni (8 not out) to successfully complete the run chase.
Pujara hit three boundaries off Glenn Maxwell to level the scores and then Dhoni hit the winning boundary to send the 25,000-odd crowd at the stadium into a frenzy.
The on-field celebrations were muted but the dressing room was delirious with joy as the players engaged in bear hugs.
The target of 155 might have looked quite a task but both Pujara and Kohli made batting look easy on a difficult track, adding 104 runs for the second wicket to pave the way for victory.
Starting the run chase, Murali Vijay (11) was bowled trying to play an unnecessary reverse sweep but Pujara played some unorthodox shots to set the tone.
India: Ajinkya Rahane, Murali Vijay, Cheteshwar Pujara, Sachin Tendulkar, Virat Kohli, Ravindra Jadeja, Mahendra Singh Dhoni (captain/wicketkeeper), Ravichandran Ashwin, Pragyan Ojha, Bhuvneshwar Kumar, Ishant Sharma
Australia: David Warner, Ed Cowan, Phil Hughes, Shane Watson (captain), Steve Smith, Matthew Wade (wicketkeeper), Glenn Maxwell, Mitchell Johnson, Peter Siddle, James Pattinson, Nathan Lyon.
Australia 1st innings: 262
India 1st innings:
Murali Vijay c Wade b Siddle 54
Cheteshwar Pujara b Lyon 52
Virat Kohli lbw Lyon 1
Sachin Tendulkar lbw Lyon 32
Ajinkya Rahane c Smith b Lyon 7
MS Dhoni c Watson b Pattinson 24
Ravindra Jadeja lbw Maxwell 43
Ravichandran Ashwin lbw Lyon 12
Bhuvneshwar Kumar not out 14
Ishant Sharma b Lyon 0
Pragyan Ojha lbw Lyon
Extras: (b 12, lb 18) 30
Total: (all out in 70.2 overs) 272
Fall of wickets: 1-108 (Pujara, 25.1 overs), 2-114 (Kohli, 27.5), 3-148 (Vijay, 40.4), 4-165 (Rahane, 45.4), 5-180 (Tendulkar, 47.5), 6-210 (Dhoni, 52.5), 7-254 (Jadeja, 63.2), 8-266 (Ashwin, 68.1), 9-272 (Sharma, 70.1), 10-272 (Ojha, 70.2)
Mitchell Johnson 17-3-44-0
James Pattinson 14-1-54-1
Peter Siddle 12-3-38-1
Nathan Lyon 23.2-4-94-7
Glenn Maxwell 4-0-12-1
Australia second innings:
David Warner lbw b Jadeja 8
Glenn Maxwell b Jadeja 8
Ed Cowan lbw b Jadeja 24
Phil Hughes lbw b Ashwin 6
Shane Watson b Ojha 5
Steven Smith b Jadeja 18
Mathew Wade c Dhoni b Ojha 19
Mitchell Johnson b Jadeja 0
Peter Siddle st Dhoni b Ashwin 50
James Pattinson b Sharma 11
Nathan Lyon not out 5
Extras (b 8, lb 2) 10
Total (all out in 46.3 overs) 164
Fall of wickets: 1-15 (Maxwell, 4.3 overs), 2-20 (Warner, 6.1), 3-41 (Hughes, 13.4), 4-51 (Watson, 17.3), 5-53 (Cowan, 18.4), 6-94 (Smith, 32.1), 7-94 (Johnson, 32.2), 8-122 (Wade, 35.5), 9-157 (Pattinson, 44.4), 10-164 (Siddle, 46.3)
Bhuvneshwar Kumar 2-0-9-0
Ravichandran Ashwin 15.3-2-55-2
Ravindra Jadeja 16-2-58-5
Pragyan Ojha 11-2-19-2
Ishant Sharma 2-0-13-1
India second innings:
Murali Vijay b Maxwell 11
Cheteshwar Pujara not out 82
Virat Kohli lbw b Lyon 41
Sachin Tendulkar lbw b Lyon 1
Ajinkya Rahane c Lyon b Maxwell 1
Mahendra Singh Dhoni not out 12
Extras (b 9, lb 1) 10
Total: (for four wickets in 31.2 overs) 158
Fall of wickets: 1-19 (Vijay, 3.3 overs), 2-123 (Kohli, 23.6), 3-127 (Tendulkar, 25.3), 4-128 (Rahane, 26.4)
Nathan Lyon 15.2-0-71-2
Glenn Maxwell 11-0-54-2
Mitchell Johnson 2-0-16-0
James Pattinson 3-0-7-0
Test debut: Ajinkya Rahane (India)
Umpires: Aleem Dar (Pakistan) and R.A. Kettleborough (England)
TV umpire: S. Ravi
Match referee: Ranjan Madugalle (Sri Lanka)
Reserve umpire: A.K. Chowdhary