Australia beat India by 333 runs on Saturday in an outstanding victory that ended the hosts' unbeaten streak of 19 Tests in the opening match of the series in Pune.
Chasing a daunting 441, the world's top side crashed to 107 all out early in the final session after left-arm spinner Steve O'Keefe's match haul of 12 wickets, handing number-two ranked Australia the upset win inside three days.
O'Keefe's heroics enabled Australia to register their first Test win on Indian soil in over a decade as they took a 1-0 lead in the four-match series.
Aussies hadn't won a match in India since 2004
The visitors last won a Test at Nagpur in October 2004, clinching the four-match series 2-1 under the then captain Ricky Ponting.
Second-ranked Australia also registered their first win in Asia after nine losses including their 3-0 thrashing in Sri Lanka last year.
Australia skipper Steve Smith rated the win as "right up there", saying: "Coming to India, we haven't won a game here 4,502 days. I have been told those facts."
"So it's been an incredibly long time...You know it's a great challenge and in this game the boys were up to the challenge," Smith told reporters.
The 32-year-old returned with impressive figures of 6-35 as he got good support from off spinner Nathan Lyon, who bagged six wickets at India's newest Test venue.
Lyon got the final wicket of Jayant Yadav (55) as the second-ranked Australian side got into a celebratory huddle.
O'Keefe made India falter twice on a turning track as another 6-35 in the first innings saw the hosts bundled out for 105.
"O'Keefe was outstanding. We've got some good players [batsmen] of spin and good spinners," said Smith.
A wily O'Keefe got the big wicket of Indian skipper Virat Kohli as he bowled the star batsman for 13, stunning the home crowd into silence.
Kohli: "They exploited the pitch better than us"
It was a rare failure for Kohli, who was out for a duck in the first innings, after scoring double hundreds in four successive series since July.
"They exploited it [the pitch] better than us. They put us under pressure throughout and deserved to win this game," said Kohli.
"We've had two really bad sessions and to pull it back against a quality side is very difficult. No excuses."
Earlier on Saturday Smith struck his first century in India before the visitors were bowled out for 285 in an extended morning session.
Smith made 109 to compound India's misery after O'Keefe had put the visitors on top on day two at Pune's Maharashtra Cricket Association Stadium.
"I rode my luck throughout the innings. I had a few lives but you need a bit of luck on a wicket like that and. I was pleased with myself to score a second innings hundred in India," said Smith.
Mitchell Starc also played a big part after scoring 61 in Australia's first innings of 260 after the visitors won a crucial toss.
Starc then took two wickets in India's first essay, getting Kohli out for nought. Starc also hit a breezy 30 in the second innings.
Young opener Matt Renshaw's gritty 68 on day one also signalled Australia's intent of putting up a show on India's home turf.
20-year-old Renshaw fought an upset stomach to score crucial runs in challenging conditions.
Second Test in Bangalore in a week's time
The teams now head to Bangalore for the second Test starting on 4 March. The final two games are scheduled in Ranchi and Dharamsala.