The Black Caps are 29 without loss after bowling Sri Lanka out for 294 runs just after lunch on the third day of the first Test at Dunedin's University Oval.
Dimuth Karunaratne made 84 and scored Dinesh Chandimal 83 to lead the way for the battling tourists.
For New Zealand, who made 431 in their first innings, Tim Southee took 3-71 and Neil Wagner 3-87 to leave Sri Lanka in trouble.
Martin Guptill and Tom Latham are still at the crease, with the openers establishing a lead of 166 at tea.
AFP/3 News