Left-arm spinner Steve O'Keefe picked up 12 wickets to guide Australia to a crushing 333-run win over India with two days to spare in the first test in Pune.
It's Australia's first win in India since 2004, and ends the home side's 19-match unbeaten streak.
The 32-year-old O'Keefe, who returned matching career-best figures of 6-35 in both innings for a maiden 10-wicket test haul, shone with the ball after his skipper Steve Smith had recorded his first test century on Indian soil to anchor Australia's batting.
India, who had not lost a home test since a 2012 defeat to England in Kolkata, were once again unable to cope with O'Keefe's probing lines after they were bundled out for a paltry 105 in the first innings.
Chasing a massive victory target of 441, India scored just two more runs in their second innings to capitulate inside three days at the Maharashtra Cricket Association Stadium, making its debut as a test centre.
"We've got to hold our heads high, take it on the chin and accept the defeat, they completely outplayed us," home captain Virat Kohli said after India fell 1-0 behind in the four-match series.
"That was probably our worst batting display in the last two years. I'm sure the guys will bounce back strongly but the batting was more disappointing than the bowling."
Arriving in India on the back of nine straight defeats in Asia, Australia were in control of the contest once they scraped together 260 in the first innings and tasted victory in India for the first time since a 342-run Nagpur victory in 2004.
"I'm really proud of the way the boys have performed in this test match," Australia captain Smith said.
"Steve O'Keefe was absolutely outstanding throughout. I think it's been 4,502 days since Australia's won a test here in India. I know it to the day and I'm really proud of that achievement."
Four of O'Keefe's six wickets in the second innings were leg before dismissals while he also got the prized scalp of Kohli, who completed a forgettable display when he shouldered arms to a straight delivery and saw his off-stump uprooted for 13.
Spin colleague Nathan Lyon provided able support, picking up the other four wickets in India's innings for 53 runs.
Earlier in the day, Smith capitalised on India's sloppy fielding with a brilliant century to help his team make 285 in their second innings after the visitors had resumed on 143 for four.
Smith, the world's top-ranked test batsman, was eventually out leg before to left-arm spinner Ravindra Jadeja for 109 after he compiled his 18th test ton to guide Australia to a winning advantage.
The 27-year-old right-handed batsman, who was unbeaten on 59 overnight, was dropped three times on Friday and was handed another lifeline on 67 but maintained his concentration on a tricky surface to bring up his 18th test hundred.
He also enjoyed another slice of fortune on 73 when a strong appeal for leg before off Jadeja was turned down by the umpire with replays indicating the decision would have been overturned on review had India not already used up their two referrals.
After Smith reached three figures with a couple of runs off Jadeja, he punched the air and planted a kiss on his helmet before soaking up the applause from the sparse morning crowd and his team mates.
Smith and Mitchell Marsh added 56 for the fifth wicket and the Australia captain contributed to two more significant stands with Matthew Wade (20) and Mitchell Starc (30) as Australia piled on the runs.
The second match starts in Bangalore from next Saturday.