New Zealand took four wickets but Karunaratne and Thirimanne made vital contributions to pilot the hosts to a six-wicket win.
Having got the 268-run target from New Zealand, Sri Lanka have started strongly as Sri Lanka have reached 133/0 at stumps on Day 4.
A fighting half-century by wicketkeeper-batsman B.J. Watling helped New Zealand to take a highly competitive lead of 177 at stumps.
Ajaz Patel picked up a five-for while Lakmal and Dickwella shared a crucial unbeaten stand of 66 to keep the home side afloat.
Akila Dananjaya takes fifer, leaves New Zealand at 203/5.
Former skipper Dinesh Chandimal and Angelo Mathews back in 15-member squad for first Test
