Playing his first match in the series, De Silva batted through pain to score 119 before retiring hurt. Debutant Silva and Niroshan Dickwella then batted out the final session as the tourists secured their second draw of the series at the Feroz Shah Kotla Stadium.
Kohli, pollution make Sri Lanka suffer
Sri Lanka, who finished on 299-5, could not chase down the 410-run victory target but played out of their skin to salvage some pride after being outplayed in the series.
India's ninth consecutive Test series triumph puts the world number one into an elite club which also includes Australia and England.
Resuming the final day on a precarious 31-3, Sri Lanka lost Angelo Mathews early in the morning session but De Silva and Dinesh Chandimal resisted India for two hours as the smog-hit Test finally saw a mostly sunny day.
India tasted success in the sixth over of the day when Mathews was caught in the slip off Ravindra Jadeja for one. Dropped three times in his first innings knock of 111, Mathews was evidently less lucky in the second, given out on a no-ball which went undetected by umpire Joel Wilson.
Record-breaker Ashwin helps India down lackluster Sri Lanka
Jadeja bowled Chandimal, then on 24, with a drifted, sharply-turning ball but replays confirmed the left-arm spinner had marginally overstepped.
Nimble-footed De Silva did not allow the situation to bog him down and scored freely, especially against the spinners, while Chandimal looked content playing the second fiddle.
Ashwin ended the 112-run partnership when he lured Chandimal out of the crease and spun it past his bat to hit the stumps. The Sri Lanka captain, who smashed a career-best 164 in the first innings, made 36.
Ashwin had a chance to catch de Silva, then on 110, off his own bowling but the off-spinner spilled the full-blooded drive. By then, De Silva was struggling with his thigh injury and the 26-year-old eventually hobbled off the field, passing on the baton to Silva, who proved equal to the challenge.
Kohli, Kumar shine as India draw first Sri Lanka Test
De Silva's third Test century contained 15 boundaries and a six off Ashwin.
Even after his exit, Silva and Niroshan Dickwella (44 not out) did not play defensively, raising 94 runs and denying India a wicket in the final session.
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