The 27-year-old replaces Ramesh Mendis despite his fellow Galle District off-spinner taking three wickets in each innings of the first Test victory.
Although Peiris was part of Sri Lanka's touring squad to Bangladesh earlier this year, he did not play. His inclusion in the national team comes on the back of notable performances in domestic cricket.
Mendis took 6-184 in the match but spin-bowling coach Craig Howard was critical of the bowlers economy rate and added of Mendis that he "hasn't played a red-ball game for a few months. He was probably a fraction off from a length-and-line point of view."
Sri Lanka made one other change from their 63-run win in the first Test, also held in Galle, with all-rounder Milan Rathnayake coming in for fast bowler Lahiru Kumara.
"One of our recent shortcomings has been the lack of contributions from the lower order, and we believe Milan Rathnayake can help address that issue," batting coach Thilina Kandamby said.
New Zealand head coach Gary Stead saw lots of positives from the opening defeat.
"We had three players (Tom Latham, Kane Williamson and Daryl Mitchell) score half-centuries in the first innings, and Rachin Ravindra's knock of 92 in the second innings was particularly impressive," Stead said. "Our focus now is on converting these promising starts into centuries."
SRI LANKA: Dimuth Karunaratne, Pathum Nissanka, Dinesh Chandimal, Angelo Mathews, Kamindu Mendis, Dhananjaya de Silva (captain), Kusal Mendis, Milan Rathnayake, Prabath Jayasuriya, Asitha Fernando, Nishan Peiris.
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