Sri Lanka, needing 363 to win, were 7-168 in their second innings at tea on the final day of the second and last Test against New Zealand at the P Sara Oval in Colombo on Thursday.
All-rounder Angelo Mathews was unbeaten on 63 at the break with Nuwan Kulasekara 18 not out.
Sri Lanka lead the series 1-0 following their 10-wicket win in the opening Test in Galle.