Australia needed just over an hour to skittle India's brittle tail and level the series in devastating fashion on day five in Perth.
Australia's tail wagged to set the Indians 287 for victory after a damaging spell after lunch saw the hosts lose 5/15 on a volatile pitch that proved almost impossible to bat on.
India needed 175 runs with just five wickets in hand to pull off a miraculous victory, but the loss of Virat Kohli late on day four clearly broke the tourist's resolve.
Australia's bowling unit combined to wipe India out for just 140 on day five — including a punishing finish where the final four wickets fell in just 15 deliveries.
The dramatic finish was a milestone moment for Aussie captain Tim Paine, his first Test victory since replacing Steve Smith as the Aussie team skipper following the infamous sandpaper scandal in Cape Town in March.
"It is probably more of a relief at the moment actually," Paine said.
"I thought the first Test win has taken a while since everything that's happened.
"I'm really proud of all our players and staff. We have worked really hard and internally we know we can keep getting better and we have been improving over the last few months.
"It is really good to get a little bit of reward. Now we turn our focus straight to the MCG."
Aussie spinner Nathan Lyon, who finished with eight wickets, was named man of the match.
India's day five collapse has also exposed deeper issues of disharmony within the Indian camp after video emerged which showed two Indian stars turning on each other as Australia romped to a memorable 146-run victory.
Channel 7 captured a heated discussion on the field between veteran paceman Ishant Sharma and star spinner Jadeja, who has been limited to drinks duty and substitute fielding in Perth.
Jadeja was controversially left out of the tourists' XI for the second Test despite Ravichandran Ashwin's injury, with the tourists opting for a four-prong pace attack.
It's unclear what Jadeja and Sharma were arguing about but it wasn't a friendly discussion.
The pair went chest to chest before two teammates, including Mohammed Shami, eventually helped restore order.
"It does seem pretty animated," Ricky Ponting said on Seven.
"There's lots of finger pointing. They were separated on a couple of occasions."
The series now heads to the Boxing Day Test at the MCG tied at 1-1.