Openers Dimuth Karunaratne and Lahiru Thirimanne were involved in a record opening stand of 133 runs.
A fighting half-century by wicketkeeper-batsman B.J. Watling helped New Zealand to take a highly competitive lead of 177.
Left-arm spinner Ajaz Patel became the first New Zealander to claim a five-wicket haul in Galle.
Dananjaya, bowling with a remodelled action after being reported for a suspect action last year, stood out with his fourth five-wicket haul.
Sri Lanka have also retained Akila Dananjaya from the list of 22 probables announced two days ago.
Chandimal was dropped from the side after poor returns in Australia where Sri Lanka suffered a whitewash under his leadership.
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