He dismissed Dwayne Bravo, Sulieman Benn and Carlton Baugh (50) as the West Indies were bowled out for 243 in their first innings at tea on the fifth and final day in reply to Sri Lanka's 387-9 declared.
With just one session left, the Test is heading for a draw. Wicketkeeper Baugh hit six fours in his second Test half-century to help his team avoid the follow-on.
The West Indies, resuming at 165-5, slipped from 205-5 to 209-8 in the afternoon session, with Herath taking two wickets and debutant paceman Suranga Lakmal one.
The tourists started the day needing 23 runs with five wickets in hand to make Sri Lanka bat again, but made them without major drama as Bravo (20) and Baugh played cautiously in initial stages.
Bravo later executed a few handsome shots, lofting Lakmal over mid-on for a four and then hitting Herath for a four and a six in the same over.
Herath got his first wicket of the innings when he had Bravo stumped in his next over after the batsman had added 44 runs for the sixth wicket with Baugh.
Skipper Darren Sammy, out for a duck in his only innings of the drawn opening Test in Galle, failed again, contributing just two runs before being caught by Angelo Mathews at square-leg while pulling Lakmal.
Benn fell for no score, caught by Tharanga Paranavitana at forward short-leg off Herath.
Baugh was on four when given out leg-before off spinner Ajantha Mendis's first delivery by umpire Richard Kettleborough, but asked for review of the decision and was then ruled not out.
He survived again when he asked for another review after being given out leg-before off Herath when on 21.
No play was possible in the morning session due to rain.