Kohli's unbeaten 104 — his 18th Test and 50th overall hundred saw India declaring their second innings at 352 for 8. This left Sri Lanka with an improbable 231 to chase in little over a session.
The target was out of reach but the Indian bowlers went full throttle raising visions of a victory, reducing Sri Lanka to 75 for 7 before umpires called off play due to deteriorating light.
Nearly 20 overs of play was still left but light was always going to be a factor as Bhuvneshwar Kumar (11-8-8-4) rocked the Sri Lankan batting in the company of Mohammed Shami (2/34 in 9.3 overs) and Umesh Yadav (1/25 in 5 overs).
After being dominated for the better part of the first four rain-truncated days, Kohli took it in his own hands to completely alter the complexion of the match.
With opposition's best bowler Suranga Lakmal (3/93) removing KL Rahul (79), Cheteshwar Pujara (22) and Ajinkya Rahane (0) within the first hour of play, the visitors were sniffing victory with India effectively 91 for 4 at that point of time.
Kohli didn't get any stable partners but initially played it safe till the lunch session before launching a ferocious counter-attack in the post-lunch session.
The two sixes over extra cover off Lakmal were a statement of intent that he was not ready to play for time trying to save the match.
Instead of being a match saving innings, it nearly turned out to be a match-winning innings as he smacked 12 boundaries and two sixes.
He assessed the pitch well knowing that survival won't help his cause and used his big front foot stride well trying to negate the swing.
The Sri Lankan bowlers especially Lakmal tried to entice him with two short covers so that he plays the uppish drive that had time and again brought about his downfall but the skipper didn't take the bait on most occasions.
There were a few streaky shots here and there but more often than not he was assertive despite not a single 50-run stand en route his hundred.
The moment he completed his hundred with a six off Lakmal's delivery, Kohli declared the innings knowing that India were certainly not going to lose from that position.
However, Sri Lanka, who were harbouring hopes of winning the game now had to bat out one full session.
Shami and Bhuvneshwar gave India a rocking start in Sri Lanka's second innings castling openers Sadeera Samarawickrama (0) and Dimuth Karunaratne (1) respectively to make it 2/2 inside four overs.
Continuing his fine first spell of 7-5-3-2, Bhuvneshwar dismissed Lahiru Thirimanne (7) in the second over after tea, while former skipper Angelo Mathews (12) was trapped leg before by Umesh Yadav to light up the proceedings with Sri Lanka 22/4.
Tempers also got flared up in the 19th over as India looked livid at the Lankans apparent time-wasting tactics when Niroshan Dickwella repeatedly went out from his crease without any disturbance with Shami beginning his run-up.
Usually cool Shami looked furious and walked straight up to the batsman as the duo had a heated exchange in the middle while Kohli too got into the act in an animated discussion before umpire Nigel Llong pacified it.
Finally, India managed to break the partnership with Shami cleaning up the Sri Lankan skipper Chandimal with a 140 -plus fuller delivery to uproot the middle-stump.
Dickwella (27) and Dilruwan Perera (0) were dismissed in addition of six runs as Bhuvneshwar and Shami looked at their furious best before the match could not last the distance.
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