Chaminda Vaas was the star as Sri Lanka recorded their first-ever Test win in the Caribbean as they beat West Indies by 121 runs to go 1-0 up in the series.
Vaas took 5-61, including the last two wickets with the new ball, as the hosts were all out for 315 just 15 minutes from the scheduled close of play.
Opener Dwayne Bravo hit 83 to take West Indies to 170-2 at lunch and give them hope of avoiding defeat.
But Sri Lanka hit back and, despite 51 not out from Chris Gayle, took the win.
West Indies seemed intent on holding out for a draw as they resumed on 96-1, needing 437 for the victory.
Ramnaresh Sarwan ably assisted Bravo with a confident 72 as the pair stretched their overnight partnership to 134, with Sri Lanka's breakthrough not arriving until just before lunch.
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Bravo drove a return catch to wickets world record-holder Muttiah Muralitharan who, after bowling for most of the day, ended with 3-112.
Vaas struck for the first time as he dismissed Marlon Samuels for 10 on 171-3 and soon landed another wicket when Shivnarine Chanderpaul was bowled off them inside edge for three.
When Sarwan was given out for lbw Sri Lanka sensed victory and Vaas bagged both final wickets.
First he forced Jerome Taylor to edge a delivery to second slip and then saw Muralitharan claim a superb one-handed catch as Daren Powell lofted a ball to mid-off.
"We had a challenge when we came and that was to win a Test match in the West Indies and we have achieved that.
"It's important that we go for a win in the second match as well, that's the way we play cricket, we want to win every Test match we play.
"That's the attitude whether it is home or away. That has served us very well in the last five to six years, that's why we've been winning Test matches away from home and we won't go away from that attitude."
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