A combo image of Ravindra Jadeja in action during the match.
In Virat Kohli's 100th Test and Rohit Sharma's first as captain, Jadeja hit an unbeaten 175 in India's 574-8 declared and then claimed a match tally of nine wickets with his left-arm spin in Mohali.
"This is my lucky ground. Whenever I come here, I always get positive vibes," Jadeja, 33, said afterwards. "I haven't done anything differently with my batting, just backing my instincts. I try to settle down and after that I play my shots. I try to keep it simple."
Jadeja, named player of the match, returned figures of 5-41 to help bowl out Sri Lanka for 174 in their first innings after the tourists resumed the day on 108-4.
Enforcing the follow-on, the hosts then dismissed Sri Lanka for 178 in the final session to lead the two-match series 1-0.
Niroshan Dickwella stood unbeaten on 51 when Ravichandran Ashwin got the final wicket of number 11 Lahiru Kumara, who was struggling with his hamstring injury, triggering wild celebrations.
Ashwin, who now has 436 scalps in 85 Tests, took four wickets in Sri Lanka's second innings and surpassed pace bowling great Kapil Dev's tally of 434 scalps.
He is now India's second highest wicket-taker behind spin legend Anil Kumble, who finished his career with 619 Test scalps.
Ashwin rattled the top-order with two wickets on either side of the lunch break as he sent back Lahiru Thirimanne for nought and Pathum Nissanka caught behind for six.
Pace bowler Mohammed Shami was rewarded for his consistency as he got skipper Dimuth Karunaratne caught behind for 27.
Angelo Mathews (28) and Dhananjaya de Silva (30) then put on 49 runs in their attempt to resist the team's quick fall before Jadeja broke the stand.
Earlier in Sri Lanka's first innings Pathum Nissanka top-scored with an unbeaten 61 and with his overnight partner Asalanka to put up some resistance in the first hour of play.
Nissanka hung on but wickets kept tumbling and Jadeja took two wickets in one over twice to send the opposition packing.
With the bat, Jadeja recorded a Test best in his second century of his career and put on marathon partnerships, including a 130-run seventh-wicket stand with Ashwin, to deflate the opposition.
Indian wicketkeeper-batsman Rishabh Pant took the attack to the Sri Lanka bowlers on day one with his quickfire 96.
Kohli made 45 in his landmark game and put on a key stand of 90 with Hanuma Vihari who made 58.
"It was a good start (to my captaincy career)," said Rohit, who replaced Kohli as captain across all formats earlier this year, saying it showed "good signs" for Indian cricket in the future.
"Credit to our bowlers who bowled in tandem and applied pressure. We knew it is a fast outfield and runs would be easier to come if you dig in. We were just waiting for an odd one to bounce differently and their batters to make mistakes," he said.
"Sometimes we were too defensive, sometimes were too attacking. Sometimes we just needed to take singles and rotate the strike and get to the other side. That's how we can play big innings," Karunaratne said.
"I think we did really well in the first two sessions of the game but once the ball got older we couldn't do well. Those are the areas we need to work on," he said.
The second match -- a day-night affair -- begins March 12 in Bangalore.
India reached 257 for six at stumps in response to England's 578 in Chennai. Washington Sundar, on 33, and Ravichandran Ashwin, on eight, were batting with an ubroken stand of 32. India need another 122 to avoid the follow-on.
Jadeja scored a career-best 175 not out as India declared its first innings at 574-8. He picked up 1-30 as Sri Lanka was reduced to 108-4 at stumps on day two.
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