India held off an Australia fightback to win the first Test in Adelaide by 31 runs.
Day five report
Shaun Marsh's 60 and lower-order resistance gave the hosts hope of recovering from 115 for five in pursuit of 323.
But Mohammed Shami, Jasprit Bumrah and Ravi Ashwin finished with three wickets each to dismiss Australia for 291.
Australia started the day requiring 219 runs with six wickets remaining.
Travis Head added just three before he was caught following a short ball from Ishant Sharma.
Marsh kept Australia's hopes alive by reaching a half-century, but fell when Bumrah found the outside edge, leaving his side on 156 for six.
Tim Paine and Pat Cummins dug deep to take Australia to within 137 runs by lunch, but the captain was caught behind for 41 in just the second over after play resumed.
Mitchell Starc joined Cummins and scored 28 from 44 balls before attempting a slog off Shami and was caught by Rishabh Pant.
Cummins also fell for 28, leaving final pair Nathan Lyon and Josh Hazlewood with a mammoth task.
At times an unlikely win seemed almost within reach as the pair combined for a 32-run stand.
But India clinched the win - and a 1-0 series lead - when Hazlewood edged Ashwin to second slip.
Day four report
Australia face an uphill task to salvage the first Test against India after ending day four requiring 219 runs with six wickets remaining.
India resumed their second innings in a commanding position on 151 for three and added a further 156 runs on Sunday in Adelaide to leave Australia chasing a target of 323.
Two wickets each for Ravichandran Ashwin and Mohammed Shami strengthened the tourists' position as the hosts lost openers Aaron Finch and Marcus Harris, as well as Usman Khawaja and Peter Handscomb, before closing on 104 for four.
Nathan Lyon, who removed India captain Virat Kohli late on day three, had earlier given Australia a chance of a comeback with a further five wickets.
Cheteshwar Pujara, who was twice given out to Lyon on Saturday but survived two reviews, was finally removed by the Australian bowler for 71 in the 88th over, caught at short leg by Finch.
Lyon also removed Ajinkya Rahane for 70 and dismissed Rohit Sharma, Rishabh Pant and Shami, while Mitchell Starc took the wickets of Ishant Sharma and Ashwin as India lost their final four wickets for just four runs.
The late implosion gave Australia hope but their top order struggled to deal with India's bowling attack.
Finch fell victim to Ashwin for just eight runs before Test debutant Harris, who was also caught by Pant, was dismissed by Shami for 26 with the second ball of the 16th over.
Khawaja sliced a Ashwin delivery into the hands of Rohit Sharma at deep extra cover and Pujara caught Handscomb at midwicket off the bowling of Shami to leave Shaun Marsh (31) and Travis Head (11) at the crease going into the final day.
Day three report
Cheteshwar Pujara was unbeaten on 40 at the end of the third day of the first Test as India built a lead of 166 over Australia with seven wickets remaining.
Pujara, who made 123 in the first innings, was twice given out to Nathan Lyon when on eight and 17, but survived two reviews to help India move into a commanding position on 151 for three.
Lyon gave hope to most in a crowd of over 30,000 at the Adelaide Oval by removing India skipper Virat Kohli (34) late in the day for a crucial breakthrough.
India began their second innings with a slender 15-run lead after restricting Australia to 235 all out and extended their advantage despite the blow of losing Kohli, caught off an inside edge by Aaron Finch, in the 58th over.
Mitchell Starc was first to strike for Australia as opener Murali Vijay was caught by Peter Handscomb for 18 to leave India on 63 for one in the 19th over.
Fellow opener KL Rahul was removed by Josh Hazlewood, caught behind by skipper Tim Paine for 44, six overs later to leave India on 76 for two and a lead of 91.
Pujara and Kohli then joined forces in a third-wicket stand of 71 to frustrate the hosts.
Earlier in the day, Australia had resumed on 191 for seven, 59 runs adrift of India's first innings 250, with Travis Head unbeaten on 61.
Head had added 11 to his overnight score when he was caught behind off Mohammed Shami, who wrapped up Australia's first innings by snaring Hazlewood in similar fashion next ball.
Day two report
Travis Head marked his home debut with an unbeaten half-century as Australia battled well on the second day of the first Test against India in Adelaide.
Chasing the tourists' total of 250, Australia fought back well to reach 191 for seven, Head finishing on 61 not out with Mitchell Starc also at the crease on eight.
It was a courageous performance from the Australians in the face of some consistent India bowling as they tried to hang on and keep themselves in contention.
India's first innings lasted just one ball on the second morning when Mohammed Shami fell to the opening delivery of the day, confirming the Australians' target.
Their task was made harder by the exploits of Ravichandran Ashwin, who took three of the first four Australian wickets after opener Aaron Finch had been bowled for a duck by Ishant Sharma.
Ashwin had Marcus Harris caught on 26 before adding Shaun Marsh for two and Usman Khawaja for 28 after lunch as he headed towards figures of three for 50 from his 33 overs.
When Peter Handscomb and Tim Paine departed in quick succession after tea, Australia looked primed for a collapse but they were settled by Head and Pat Cummins who forged a 50-run partnership.
With Head still at the crease at the close of play, the Australians had managed to withstand the barrage and give themselves hope heading into the third day.
Day one report
On a day where it touched 40 degrees in the middle at the Adelaide Oval, Pujara provided almost half the runs in India's 250 for nine.
Pujara made 123 from 246 balls before falling to what proved to be the last ball of the day, stranded by a brilliant direct hit from Pat Cummins.
It was a monumental effort from the 30-year-old after India had slumped to 41 for four, with the top-order guilty of some careless batting.
Openers Lokesh Rahul (2) and Murali Vijay (11) fell before India picked up the prize wicket of Virat Kohli.
The India captain had only made three when he chased a full and wide delivery from Cummins and was brillaintly caught by Usman Khawaja in the slip cordon.
Ajinkya Rahane (13) also departed quickly before Pujara rebuilt the innings in tandem with Rohit Sharma (37), Rishabh Pant (25) and Ravichandran Ashwin (25).
But Nathan Lyon's wily off-spin kept Australia on top and he took the wickets of Sharma and Pant to return figures of two for 83 from 28 overs.
Pacemen Mitchell Starc, Josh Hazlewood and Cummins also finished the day with two wickets apiece.
Pujara went scoreless for a period of 29 deliveries on 11, but his patience was just what India required as the visitors edged towards respectability.
He was fortunate on 89 when replays suggested he got a nick to wicket-keeper Tim Paine on an attempted cut off Hazlewood, but Australia did not review.
Pujara punished Australia for that error by moving to 99 with successive legside blows off Hazlewood before clipping Starc wide of mid-on to reach three figures.
Cummins' brilliance finally ended his resistance and gave Australia a definite advantage heading into day two.