England lose two wickets after steady start against India
England were 67 for two in Chennai with Dom Sibley on 26 and skipper Joe Root on four in his 100th Test, after winning the toss at the start of the four-match series.
Burns, a left-hand batsman, fell to off-spinner Ravichandran Ashwin for 33 while attempting a reverse sweep. The opening pair put on 63 runs.
Paceman Jasprit Bumrah, who is playing his first Test at home, struck soon after to send back new batsman Dan Lawrence for nought.
Earlier the left-right batting combination of Burns and Sibley used their feet to good effect against spinners Ashwin and Shahbaz Nadeem.
Ben Stokes, Jofra Archer and Rory Burns return to the team in Chennai after making it back to the squad for the four-Test series.
"I do enjoy playing cricket in India," said the 30-year-old Root. "I am looking forward to a great series. We have to play at our best and we are very confident."
Root received his 100th Test cap from Stokes while wicketkeeper-batsman Jos Buttler received his 50th Test cap from the captain before the game.
For India, Virat Kohli returns to lead the side after missing most of the Australia Tests, which the tourists won 2-1, on paternity leave.
Left-arm spinner Shahbaz Nadeem makes the team after being added to the squad on Friday morning in place of Axar Patel, who was ruled out with a knee injury.
"It was an amazing phase for us, having a child is an amazing feeling and combined with the way the team played in Australia," said new dad Kohli.
"We are not thinking about the Test championship at the moment, just take one game at a time."
The Test is India's first home international since the South Africa one-day series was abruptly cut short due to rising coronavirus cases in the country in March last year.
The series will decide who plays New Zealand in the final of the inaugural world Test championship.
The match will be played behind closed doors but fans to be allowed into the second clash in Chennai.
India: Virat Kohli (capt), Rohit Sharma, Shubman Gill, Cheteshwar Pujara, Ajinkya Rahane, Rishabh Pant, Washington Sundar, Ravichandran Ashwin, Ishant Sharma, Jasprit Bumrah, Shahbaz Nadeem
England: Joe Root (capt), Rory Burns, Dominic Sibley, Daniel Lawrence, Ben Stokes, Ollie Pope, Jos Buttler, Dominic Bess, Jofra Archer, Jack Leach, James Anderson