Herath´s 5/139 and Kiwi captain Daniel Vettori´s century was the highlight of the fifth day in which the visitors kept the hosts frustrating till the prolonged second session.
Given a mammoth target of 494 to win, New Zealand posted 397. In the first innings they were bowled out for 234 after Sri Lanka posted 416. Sri Lanka declared their second innings at 311/5.
Vettori, out as last man, made 140 - his personal best - but was unable to save the match.
Resuming the fifth day at 182/6, Vettori and Jacob Oram kept the New Zealand hope of salvaging a draw alive until Tilakratne Dilsan snapped the 124-run partnership dismissing Oram (56) just before lunch.
Iain O´Brien played a gusty knock adding 78-run with Vettori. O´Brien scored only 12 but stayed 75 balls before becoming the fifth victim of Herath caught behind.
Earlier on the Test, Sri Lanka opted to bat first and went on scoring 416 in the first innings.
Thilan Sameraweera, who was later adjudged man of the series, scored 143 while unlucky Mahela Jayawardene was out on 92. Kumar Sangakkara too scored 50 in the innings.
Jiten Patel took four wickets while Vettori got three in Sri Lanka´s first innings.
Spinners caused trouble for New Zealand in their first innings as Herath and Muttiah Muralitharan each grabbed three wickets to bowl out the visitors for 234. Apart from Ross Taylor (81), no other batsmen scored more than 35.
In the second innings, Sri Lanka posted 311/5 - thanks to Sangakkara´s 109 and Jayawardene´s 96. Jayawardene was adjudged man of the match.
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