Adelaide - India won their first Test on Australian soil in a decade on Monday, bowling out the home side in a nail-biting finale to clinch the opening match of the series at Adelaide Oval with Rishabh Pant equalling a world-record along the way.
The hosts were set an improbable target of 323, which would have been a record run chase at the ground but gallantly battled to 291 before Josh Hazlewood became the last man to fall to Ravichandran Ashwin, who finished with 3-92. Shaun Marsh made 62 and Tim Paine 41.
Wicketkeeper Pant made history by matching the record 11 catches in a Test currently held by England's Jack Russell and South Africa's AB de Villiers.
In doing so, he beat the record 10 catches in a game by an Indian that was previously held by Wriddhiman Saha.
It was a huge breakthrough for Virat Kohli's men, with Australia always proving a tough hunting ground.
The last Test they won in Australia was at the WACA Ground in Perth in 2008, and the last one in Adelaide was 2003, with just six victories now in more than 70 years - and never one in the first match of a series Down Under.
Another blot on Indian cricket history is that they have never won a series in Australia.
But with the home team missing the banned Steve Smith and David Warner, Kohli and his team sensed ahead of the tour that this could be their opportunity to make history.
They now take the momentum into the second Test in Perth starting Friday, with Melbourne and Sydney to follow.
Australia resumed the final day needing another 219 for victory with four wickets down, but lost their last two specialist batsmen before lunch, shifting the odds heavily in India's favour.
Marsh and Travis Head had started cautiously, grinding out 11 runs in the opening seven overs before seamer Ishant Sharma struck with the score on 115, bowling a bouncer that caught Head's bat as he tried to fend it off and Ajinkya Rahane took the catch at gully.
Paine joined Marsh and they upped the ante, capitalising on some loose balls from Shami to chip away steadily and close the gap.
Marsh brought up a valuable 50 - his 10th in Tests - with a boundary from a pull shot off spinner Ashwin.
It was a much-needed knock for the left-hander, who was on a run of six consecutive single-figure Test scores, although he has been in scintillating form in domestic cricket.
But he didn't last much longer with Jasprit Bumrah getting the big breakthrough as Marsh pushed at a perfectly angled delivery, getting a faint edge to Pant behind the stumps.
By lunch Australia had fought to 186 for 6, still needing a further 137 runs for victory, with Paine not out 40 and Pat Cummins on five.
But in the second over after they resumed Paine top edged a pull shot from Bumrah and Pant easily took a catch.
Cummins, who survived two big reviews within four balls, with the technology both times going in his favour, showed fantastic application with Mitchell Starc in a 41-run eighth wicket stand.
And when the runs needed dropped below 100, the crowd dared to dream before Starc fell to Shami for 28. It brought Nathan Lyon to the crease and he got the pulses racing with a quick 38 to set up a tense finale before Hazlewood departed.