Warrican mopped up the Sri Lankan tail to dismiss the home team for 200 after tea after the West Indian pace attack had wreaked havoc on the home team's top order in the first two sessions.
When play was halted early because of fading light and the threat of rain, West Indies were 17-1 in reply.
Jerome Taylor, who came through a late fitness test after concerns about a groin problem, and skipper Jason Holder each took two wickets as the tourists' pace and bounce hurt Sri Lanka from the start of play.
Only Milinda Siriwardana, playing in only his second test, made a significant contribution with the bat, top-scoring with a patient 68 off 111 deliveries.
Taylor inflicted the first wound, striking with the fourth ball of the morning to dismiss Kaushal Silva, caught behind for a duck, after the tourists successfully reviewed the not-out decision of the umpires.
Opener Dimuth Karunaratne (13) was next to go in the 10th over after Holder trapped him leg before with an angled delivery from around the wicket, which the Sri Lankan failed to overturn after asking for a review.
Debutant Kusal Mendis followed three balls later after another successful review by the West Indies, leaving the hosts teetering on 34-3. The 20-year-old batsman, starting ahead of out-of-form Lahiru Thirimanne, wafted at a delivery from Kemar Roach to go for 13.
Sri Lanka skipper Angelo Mathews (14) then fell just before the lunch break when he edged a Holder delivery to Kraigg Brathwaite at second slip, which again required television replays before the decision was ratified.
The 23-year-old Warrican picked up his first test wicket before tea when he caught and bowled Kusal Perera for 16 then returned after the break to dismiss Siriwardana, Dhammika Prasad and finally Nuwan Pradeep.
West Indies lost opener Shai Hope in the first over, trapped lbw by Prasad for four, but survived to stumps without any additional casualties.
(Writing by Patrick Johnston in Singapore and Julian Linden in London; Editing by Peter Rutherford, Neville Dalton)
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