The American they will face Australia and Serbia on July 15 and July 17 as part of their preparation for the Paris Olympic Games
Only 36.3 overs were possible after rain washed out the first session and bad light ended play for the day with Karunaratne unbeaten on 49.
Karunaratne, fresh from a match-winning century in the first Test in Galle last week last week, hit six boundaries during his 100-ball stay in overcast conditions.
Former captain Angelo Mathews was giving Karunaratne company in the middle to remain unbeaten on nought after facing 14 deliveries.
New Zealand all-rounder Colin de Grandhomme, who made the XI in place of Mitchell Santner, said the match was "evenly poised".
"There's a bit of more bounce on this track than what we encountered in Galle and that's nice," he said after play ended.
"If we can get a couple of early wickets tomorrow morning that will be nice."
Karunaratne batted with positive intent despite losing opening partner Lahiru Thirimanne and Kusal Mendis either side of tea.
Thirimanne never looked comfortable and his 59-minute stay at the wicket produced just two runs.
His misery ended when he pushed a William Somerville delivery and was caught at extra cover by skipper Kane Williamson. He had been earlier dropped by wicketkeeper B.J. Watling off Somerville.
Mendis looked good as he reached 32 with four fours and put on 50 runs with Karunaratne to steady the batting.
De Grandhomme got Mendis caught behind on a seaming delivery outside the off stump and Watling gloved the catch.
"I was just trying to be patient and stay for a longer period operating in the same line until he made a mistake and he did that, and we were glad to claim that wicket just before close of play," de Grandhomme said.
The hosts only need a draw to clinch the two-match series.
Both teams made one change from the first match.
Sri Lanka included veteran spinner Dilruwan Perera in place of Akila Dananjaya, who was reported for a suspect bowling action after the first Test.
The entire opening session and another hour was lost due to persistent rain and the toss took place at 1:10 pm (0740 GMT). The afternoon session went uninterrupted but play was again delayed by 28 minutes after tea due to rain.
After 7.3 overs in the evening session, play was called off due to bad light.
Play will resume on day two 15 minutes before schedule at 5:15am UAE Time.Hosts on top
Sri Lanka
D. Karunaratne not out 49
L. Thirimanne c Williamson b Somerville 2
K. Mendis c Watling b de Grandhomme 32
A. Mathews not out 0
Extras (b1, lb1) 2
Total (2 wickets, 36.3 overs) 85
Did not bat: K. Perera, D. de Silva, N. Dickwella, D. Perera, S. Lakmal, L. Embuldeniya, L. Kumara
Fall of wickets: 1-29, 2-79
Bowling: Boult 7-2-20-0, Southee 12-4-22-0, De Grandhomme 8.3-2-14-1, Somerville 6-3-20-1, Patel 3-1-7-0
Toss: Sri Lanka
Umpires: Michael Gough (AUS) and Bruce Oxenford (AUS)
TV umpire: Richard Illingworth (ENG)
Match referee: Andy Pycroft (ZIM)
The American they will face Australia and Serbia on July 15 and July 17 as part of their preparation for the Paris Olympic Games
The leaders emphasise that the deal to release the hostages would bring an immediate and prolonged ceasefire in Gaza
Dubai-based Sumit Augustine has had a philosophical approach towards spending
The regional upswing also defies oil production cutbacks
It's a treatise that would determine the course of your life, not just academically, but as a person too
A US-based company is developing an eVTOL aircraft for commercial passenger service and is expected to start operations by 2025 or early 2026
The project’s aim is to generate funds for Harmony House, an orphanage located in India's Gurgaon
Earlier, the Emergency, Crisis and Disaster Management confirmed the reopening of all roads in the emirate