India have already taken a 44-run lead in the first innings with eight wickets remaining in reply to Sri Lanka's 183 all out.
At lunch, Dhawan was batting on 110 (198b, 11X4) and Kohli was unbeaten on 86 (156b, 9X4), having shared an unbroken 199-run stand for the third wicket.
The two overnight batsmen kept the Sri Lankan bowlers wicketless throughout the first session of day two.
With the predicted rain showers staying away, the two batsmen had the task cut out ahead of them. They gave a solid start to the session, even as the pitch was very different from how it behaved in the first session yesterday.
Kohli got going quickly and brought up his 11th Test half-century off 90 balls in the 38th over, fourth of the morning. He had an interesting duel with Rangana Herath (40/0), who had a couple good LBW shouts against the batsman, but the Indian captain made sure that he planted his front-foot just outside the bowler's line and put that mode of dismissal out of context.
At the other end, Dhawan was scoring quickly enough in comparison to his partner, but by his own standards, it was a watchful and sedate innings. He survived a close call for LBW in the 49th over, on 79, when Tharindu Kaushal (78/0) seemed to have trapped him after the ball pitched inside leg-stump and appeared to be hitting the middle one.
There were no further half-chances coming for the hosts thereafter as Dhawan-Kohli settled down after an engaging first hour of play that yielded 41 runs.
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