Debutant off-spinner Nishan Peiris claimed six wickets on Sunday to secure Sri Lanka's first series victory against New Zealand in 15 years with a dominant win by an innings and 154 runs in the second Test in Galle.

New Zealand were dismissed for 360 in their second innings before tea on day four after being forced to follow-on. Peiris, 27, and fellow spinner Prabath Jayasuriya combined for 18 wickets in the match, with the latter taking 6-42 in the first innings to dismiss the tourists for just 88 after the hosts had posted a massive 602-5 declared.

"It's amazing how the batting unit rose to the occasion," Sri Lanka captain Dhananjaya de Silva told reporters. "Then the spinners were too good... Once we bowled them out for less than 100 runs in the first innings, it was very difficult for them to come back into the game."

New Zealand's lower order showed some resilience after resuming at 199-5 on Sunday, with Tom Blundell, Glenn Phillips, and Mitchell Santner all scoring half-centuries. Peiris, who had taken three second-innings wickets on Saturday, trapped Blundell lbw for 60 early in the first session, ending a 95-run stand with Phillips. Santner helped forge a 64-run partnership for the seventh wicket before the determined Phillips fell on 78 when he mistimed a shot to long-on, giving Peiris his maiden five-wicket haul.

Santner then put together a stubborn ninth-wicket stand of 53 with Ajaz Patel before the latter was sent back, bowled by Jayasuriya, on 22. Sri Lanka sealed the victory when Santner's gritty resistance was finally broken, stumped by Kusal Mendis for 67 off Peiris.

"Galle is a tough place to come and play cricket and Sri Lanka are a strong team here," said New Zealand captain Tim Southee. "We were on the wrong side of the toss and we struggled to make the breakthroughs. We really struggled to come back from there," he added.

Sri Lanka could have wrapped up the match and series in the morning session but for a succession of dropped catches. Kamindu Mendis spilled Patel on two at second slip and let Santner off on 36 in the covers. Peiris shelled another chance from Santner not long after.

Sri Lanka won the opening match by 63 runs, and this series win is their first against New Zealand since a 2-0 win at home in 2009. The result leaves New Zealand winless from six Test appearances at Galle, with Sunday's 360 their highest innings total at the venue.