Indies never managed to build enough momentum to challenge the hosts.
Jermaine Blackwood, the last man out for 92, put up a resistance, but not enough to stave off an innings defeat. His knock included 10 fours and three sixes.
Shortly after the start of the day’s play, nightwatchman Devendra Bishoo was caught by captain Mathews off the bowling of Herath with the score at just 74.
The next ball, Herath trapped Marlon Samuels leg before wicket.
Though the spinner missed out on a hat-trick, Sri Lanka kept the West Indies in trouble with Darren Bravo (31) falling to a peach of a swinger by Nuwan Pradeep that edged back to wicketkeeper Kusal Janith Perera.
Denesh Ramdin was next to fall, caught at slip off the bowling of Milinda Siriwardana.
In reply to Sri Lanka’s 484, the West Indies’ batsmen were no match for Herath’s guile.
The young opening pair of Kraigg Brathwaite and Shai Hope looked confident at the start, but were ill-equipped to absorb the pressure from Herath.
Marlon Samuels — of whom much was expected — failed in both innings, scoring 11 in the first and falling for a first ball duck in the second. Darren Bravo flourished briefly in both innings, with a top score of 50 in the first and 31 in the second. He then fell in a soft dismissal reflecting the inability of the Caribbean team to play the longer innings required to save the Test.
The rest of the Sri Lankan bowling backed up Herath well perhaps with the exception of Tharindu Kaushal. The 22-year-old tested recently for suspect action and cleared later to bowl other than the doosra appeared clearly to have been mentally hit.
For Sri Lanka it was the launch of the new era after the exit of the legends, Mahela Jayawardene and Kumar Sangakkara. It will also be a welcome return to the winning ways after their series defeats to both Pakistan and India at home.
“We had chances and we did not take them,” said West Indian captain Jason Holder. “Hopefully we can set things right in the next game.”
Score Board
Sri Lanka won toss
Sri Lanka 1st innings 484 all-out (F Karunaratne 186, L Chandimal 151; Bishoo 4-143)
West Indies 1st innings 251 all-out (D Bravo 50; Herath 6-68)
Score Board
West Indies 2nd innings (follow on)
K C Brathwaite lbw b Herath 34
S D Hope b Siriwardana 6
D M Bravo c Perera b Pradeep 31
D Bishoo c Mathews b Herath 10
M N Samuels lbw b Herath 0
J Blackwood c Silva b Prasad 92
†D Ramdin c Silva b Siriwardana 11
*J O Holder run out 18
K A J Roach st Perera b Herath 5
J E Taylor lbw b Prasad 5
S T Gabriel not out 7
Extras (lb 3, w 2, nb 3) 8
Total (all out; 68.3 overs) 227
Fall: 1-18, 2-60, 3-74, 4-74, 5-88, 6-136, 7-172, 8-178, 9-189, 10-227
Bowling: Prasad 9.3-3-28-2 (2nb, 2w); Herath 22-5-79-4; Pradeep 14-1-28-1; Siriwardana 12-1-60-2; Kaushal 11-3-29-0 (1nb)
Result: Sri Lanka won by an innings and 6 runs
Series: Sri Lanka lead the 2-match series by 1-0
Test debut: T A M Siriwardana (Sri Lanka)
Man of the Match: H M R K B Herath (Sri Lanka)
Umpires: M Erasmus (South Africa) and R K Illingworth (England). TV umpire: S D Fry (Australia). Match referee: D C Boon (Australia)