India 572 (Dhoni 224, Pattinson 5-96) and 50 for 2 beat Australia 380 (Clarke 130, Ashwin 7-103) and 241 (Henriques 81*, Ashwin 5-95, Jadeja 3-72) by eight wickets
Scorecard and ball-by-ball details
An Indian victory that seemed imminent minutes after tea on day four was eventually completed by Sachin Tendulkar, 40 minutes before lunch on day five. Australia's resistance over that period arrived too late to change the result, but in it may be found the clues to a tighter contest when the second match begins in Hyderabad on Saturday.
MS Dhoni, R Ashwin, Virat Kohli and Tendulkar were the pivotal contributors to India's 1-0 series lead, showing greater discipline and awareness of the sort of cricket best played on the MA Chidambaram Stadium's clay court. Save for Michael Clarke's first-day century and James Pattinson's fiery pace, it was not until Moises Henriques stood up with the bat in the second innings that the tourists showed evidence of catching up.
A target of only 50 to win was reached with the help of some Tendulkar fireworks - towering sixes from his first two deliveries against Nathan Lyon - but Pattinson again bowled well to the openers and Lyon showed far greater consistency of line and control of length than he had managed while being taken for 3 for 215 in the first innings.
India were left with some questions about their opening pair, M Vijay and Virender Sehwag doing little in either innings, and they may also wonder about subtracting another seam bowler from their XI should the Hyderabad surface be anything like this one. Australia have found a steady batting hand in Henriques, but much of their display in this match will be the cause of serious introspection.
Henriques and Lyon had put on 66 for Australia's last wicket, a defiant gesture after the earlier batsmen had failed to stand their ground. Henriques' unbeaten innings completed a fine double for the debutant, who has surely made his place safe for the second Test.
Ultimately it was Ravindra Jadeja who ended the stand after 25 minutes on the final morning, switching from over to around the wicket against Lyon and coaxing an inside edge onto pad that was snapped up by short leg.
Pattinson's first ball of the innings was a snorter, pitched short and seaming back sharply at Vijay, though it angled away from Matthew Wade and flew away for four byes. The ball kept Vijay thinking, and after depositing Lyon for one straight six, he fell when an indecisive drive was well taken by Henriques at a shortish mid-off.
In the next over Cheteshwar Pujara offered a sharp chance when padding up to Lyon, the ball striking pad and glove but eluding Wade, who was unable to adjust to the ball's shifting trajectory. Sehwag sliced a brace of boundaries over the slips cordon from Pattinson, and when Peter Siddle replaced him he drove sweetly down the ground.
Lyon, meanwhile, showed some evidence of improvement in his bowling. He twirled down far fewer deliveries that could be tucked around the corner behind square leg, and the better line forced some impatient premeditated strokes from Pujara. It also undid Sehwag when he snicked to Clarke at slip. This little joust was ultimately immaterial to the result, sealed as it was by Tendulkar's sixes, but demonstrated that Lyon was learning.
Daniel Brettig is an assistant editor at ESPNcricinfo. He tweets here