The Kiwis bowled Sri Lanka out for a second innings total of 195 in the last session of the fifth and final day at the P Sara Oval to win the second and final Test by 167 runs.
All-rounder Mathews offered dogged resistance, top-scoring with a fighting 84 that included one six and 11 fours before he was the last man dismissed after facing 228 balls.
New Zealand, who had lost five successive Tests before the match, put in an improved all-round show in Colombo, posting 412 in the first innings and their bowlers, especially the pacemen, delivered in both innings.
Pics: Prabhas, Tamannaah Bhatia at 'Baahubali 2' first look launch at MAMI
'Ae Dil Hai Mushkil' photos: Aishwarya, Anushka, Karan get candid at MAMI
Photos: Huma Qureshi, Neha Dhupia and other celebs at MAMI
Photos: Amy Jackson, Daisy Shah at Mumbai airport
Photos: Sridevi, Irrfan and other celebs at 'Mughal-e-Azam' screening