Third Test, Perth: India 330 & 294 bt Australia 212 & 340 by 72 runs (day four)
RP Singh sparked scenes of unbridled jubilation by bowling Tait
India denied Australia a record 17th straight victory by dismissing them for 340 to win the third Test by 72 runs.
Resuming on 65-2, chasing 413, the hosts did well to only lose Ricky Ponting (45) on the fourth morning.
But Mike Hussey (46), Andrew Symonds, Adam Gilchrist and Brett Lee fell to make it 243-7 at tea, while Anil Kumble had Michael Clarke (81) stumped.
Mitchell Johnson (50no) shared 73 with Stuart Clark (32) but India persevered to cut their series deficit to 2-1.
It ended the home side's hopes of surpassing the 16 consecutive victories achieved by Steve Waugh's Aussies between 1999-2001.
The defeat was their first since the thriller at Trent Bridge against England in 2005, and their first on home soil since India beat them in Adelaide in 2003.
And the tourists will now fancy their chances of completing their fightback in the finale at the same South Australia venue and emulate the series draw they achieved that time.
That is a remarkable prospect considering the acrimony and soul-searching which followed their controversial defeat in Sydney.
Australia were hoping the Waca pitch, which had shown signs of variable bounce and turn would hold up well in the baking heat.
However, their chances suffered an early blow when captain Ponting was caught by Rahul Dravid at first slip off Ishant Sharma, and the middle order fell away after lunch.
Hussey was trapped lbw by RP Singh and Symonds was leg-before to skipper Kumble although replays showed he had made contact with the bat.
Part-time spinner Sehwag then did further damage by bowling Gilchrist round his legs for 15 and having Lee snapped up at silly mid-off by VVS Laxman.
Clark and Johnson swung the bat merrily to frustrate the Indians
While Clarke was at the crease the Aussies retained an outside chance of a stunning success.
But his 134-ball defiance ended when he charged down the track to leg-spinner Kumble and was a couple of yards short when Mahendra Dhoni whipped off the bails.
India's celebrations were delayed by an unlikely obstacle in Johnson, who smashed Sehwag over mid-on for six and clubbed three fours in one Kumble over costing 17 runs.
Johnson was bowled off a Kumble no-ball and dropped on the boundary at wide long-on by Sehwag before clubbing a massive six in the same region to bring up the fifty partnership off 47 balls.
The visitors were losing their grip, on the ball and their nerves, as edges and heaves dropped agonisingly short of fielders.
Singh was handed the second new ball at the first opportunity and Clark, who was fed a steady diet of long-hops, promptly pulled him for another maximum to bring the target down to 100.
The tail-enders' confidence was soaring but Pathan found Clark's edge to have him caught behind.
Johnson, who was dropped by Dravid at first slip off Singh, deservedly reached his maiden Test fifty off 80 balls but Singh clean bowled Shaun Tait to seal a momentous Indian triumph.
Australia have been fined for their slow over-rate at the Waca. Skipper Ricky Ponting was docked 20% of his match fee, while the rest of this team were fined 10%.