He drove fluidly and cut strongly, particularly late in his innings, before being bowled by a terrific ball from left armer Trent Boult which pitch on his middle stump and moved away a fraction to bend his off stump back.
Niroshan Dickwella didn't last long and debutant Kaushal hung on in the last couple of overs, with captain Brendon McCullum setting eight fielders between first slip and square gully.
Mathews completed his second half century of the match and Sri Lanka's chances of being competitive tomorrow rest with him.
New Zealand worked hard and generally impressively. The ball regularly beat the defensive stroke and offspinner Mark Craig caused problems with turn and bounce.
A couple of half chances went begging and Karunaratne survived two referrals by New Zealand, although in both cases, at 83 and 103, the decision was correct.
Boult finished the day with three for 62 while Tim Southee and Jimmy Neesham had one wicket apiece.
Sri Lanka will start the fourth day 10 runs behind.