Sri Lanka clinched a 121-run win, their first ever in the West Indies, with just 40 balls of the first Test to spare in Guyana.
Chasing an unlikely victory target of 437, the West Indies started the final day on 96-1, requiring a further 341, and realistically the aim was to use the nine wickets left to bat out for a draw.
Dwayne Bravo and Ramnaresh Sarwan offered the most resistance and skipper Chris Gayle, opting to come in at six, finished unbeaten on 51 as his side were all out for 315.
Sri Lanka's experienced left-arm seamer Chaminda Vaas did the damage with five wickets, but the home side still had chances to save the game with two wickets intact inside the final 11 overs.
Jerome Taylor was caught in the slips and, with just 6.4 overs left to play, last man Daren Powell played an ill-advised drive which looped up into the air and Muttiah Muralitharan, pedalling back furiously from mid-off, took a superb diving one-handed catch to end the game.
Bravo had made the most of opening the batting by compiling a fine 83 before he became the second wicket to fall when he was caught and bowled by Muralitharan.
Vaas then had his first say when he quickly got rid of Marlon Samuels (10) and Shivnarine Chanderpaul (3) and to reduce West Indies to 178-4.
That became 212-5 when Thilan Thushara (2-70) trapped Sarwan lbw to end a 206-ball vigil ended worth 72.
Although Gayle was batting confidently, he could not find anyone to hang around as Ryan Hinds (10), Denesh Ramdin (1) and Sulieman Benn (7) all came and went.
No.10 Taylor (12) put on 47 with his captain before departing with 10.5 overs left to play, caught at second slip to become Vaas' fourth wicket.
Gayle brought up his half-century with eight overs left, but at the other end Powell was flashing away, and he was fortunate to be given not out by umpire Simon Taufel after gloving Vaas through to the wicketkeeper.
Sri Lanka skipper Mahela Jayawardene had a word in Powell's ear and it did the trick as he lost his head soon after.
Attempting to drive Vaas back over his head, Powell could only loft the ball gently into the air where mid-off fielder Muralitharan seemed to be flapping underneath it. That was until he leapt in the air and stuck out his right arm to take a stunning one-handed catch to end the game.
Vaas finished with 5-61 in the innings and eight wickets in the match as Sri Lanka deservedly enjoyed a maiden Test win in the Caribbean by a margin of 121 runs.
The second and concluding Test of the series starts in Trinidad next Thursday, live on Sky Sports.