Herath inflicted more misery on the hapless touring side by dismissing opener Kraigg Brathwaite lbw for 34 in West Indies' second innings and they finished the day on 67 for two, still needing 166 runs to avoid an innings defeat.
Shai Hope (six) was the other opener out when he was bowled by Milinda Siriwardana to become the debutant all-rounder's first test victim.
Darren Bravo (20) and nightwatchman Devendra Bishoo (six) were at the crease at stumps.
Bravo (50) had offered resistance in the first session too, making his 12th half-century in tests before falling to Herath, Dinesh Chandimal completing a brilliant acrobatic catch at mid-wicket to dismiss the left-hander.
Herath struck in his second over of the day with an innocuous delivery which Marlon Samuels (11) made a mess of.
The batsman failed to connect on a pull shot and the ball, going way down the leg side, hit his thigh and went on to disturb the stumps.
Jermaine Blackwood (11) did not last long either, edging Dhammika Prasad to Siriwardana at slip where the fielder juggled a catch but held on.
Jason Holder (19), leading the side for the first time in tests, gave Prasad his second wicket when he edged behind to wicketkeeper Kusal Perera after hitting the paceman for two consecutive boundaries.
Wicketkeeper Denesh Ramdin fell in similar fashion to fast bowler Nuwan Pradeep before Kemar Roach, who was dropped on five by Sri Lanka captain Angelo Mathews at slip off Herath, and Jerome Taylor (31) launched a counter-attack.
Taylor hit four boundaries and a six in his 31-ball knock and his 46-run stand for the eighth wicket with Roach gave West Indies hope of saving the follow-on.
Roach (22) also added 34 with Bishoo for the ninth wicket but Herath ensured they fell short by dismissing him and Shannon Gabriel off successive deliveries shortly after tea.
(Reporting by Sudipto Ganguly in Mumbai; Editing by Ed Osmond)
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