Sri Lanka clung on to draw the first Test against India after Bhuvneshwar Kumar went close to inspiring a sensational last-day win for the hosts in Kolkata.

After Shikhar Dhawan and KL Rahul led a fourth-day recovery for India, captain Virat Kohli scored his 50th international century - naturally in record fashion - to give the hosts a faint sniff of victory with a session and a bit to bowl Sri Lanka out.

Kohli reached three figures with a six before India declared on 352-8, setting their opponents 231 to win with 40 overs remaining.

With bad light bringing the previous four days to a premature close, it never looked likely, but Bhuvneshwar delivered a brilliant performance, taking 4-8, while Mohammed Shami took two more wickets in a blistering support act to reduce Sri Lanka to 75-7 from just 26.3 overs before the light curtailed any further excitement.

After having the best of the first three days in this contest, such a collapse will not do Sri Lanka's confidence any good as the three-match series next heads for Nagpur.

But India will be brimming after the performances of their bowlers and captain Kohli, whose half-century of international hundreds came in his 348th appearance - level with the record-holder, Hashim Amla.

In worsening conditions for batting, Kohli's knock oozed class, displaying not only his apex technique but also battling qualities.

The skipper got off a pair as he gloved Suranga Lakmal over wicketkeeper Niroshan Dickwella for four, but the Sri Lanka paceman was causing Kohli and Cheteshwar Pujara - who batted on every day of this Test - serious problems, having earlier bowled Rahul for 79.

Lakmal finally had his reward taking Pujara (22) and Ajinkya Rahane (0) in the same over, and Kohli regularly lost partners while scratching his way through his innings.

But Sri Lanka's decision to immediately take the new ball backfired as Kohli accelerated from 58 of 93 balls to a century from just 26 more, spanking Lakmal over extra cover and then heading to the dressing room.

After heavy rain on day one, India had been reduced to 50-5 on the second morning of this Test, but incredibly had a chance of winning the contest when Bhuvneshwar and Shami reduced Sri Lanka to 22-4 inside 12 overs.

Knocks of 20 from Dinesh Chandimal and 27 by Dickwella would ultimately prove vital, just holding the Indian charge up enough.

Dickwella survived a catch behind on review and Dilruwan Perera survived a DRS for lbw before Bhuvneshwar flattened his off-stump, but umpires Nigel Llong and Joel Wilson convened midway through the 26th over with the light meter before Kohli shook hands with the Sri Lanka batsmen, who had escaped an almighty scare.