Vaas took 5 for 61 in 22.2 overs, while prolific leg-spinner Muttiah Muralitharan snared 3 for 112 from 45 overs, as the West Indies, chasing an unlikely 437 for victory, were dismissed for 315 in their second innings just 5.4 overs before the scheduled close of play.
Fittingly, the pair combined to finish the match when Vaas delivered a rising ball to Windies tail-ender Daren Powell who tried to chip a back-pedalling Muralitharan at mid-off, with the spinner holding a remarkable catch.
|"We played hard and a lot of guys contributed. It was an amazing effort from Chaminda Vaas... "|
Sri Lanka captain
"We had a challenge when we came and that was to win a Test match in the West Indies and we have achieved that," Mahela Jayawardene, Sri Lanka captain, told reporters.
"We played hard and a lot of guys contributed. It was an amazing effort from Chaminda Vaas, and our quicks took 13 wickets in the Test, so a lot of credit to them.
"Muttiah Muralitharan bowled his heart out, and overall it was a very good team effort."
The victory did not come easily for Sri Lanka, as Dwayne Bravo, Ramnaresh Sarwan, and West Indies captain Chris Gayle all made half-centuries to extend the home team's innings deep into the final day.
Bravo top-scored with 83, Sarwan, who hit his second half-century of the match made 72, and Gayle, batting down the order, made an unbeaten 51 at the Guyana National Stadium.
Sri Lanka also benefitted from some dubious umpiring decisions, when Ryan Hinds was given out caught behind from a Muralitharan delivery that went wide down the leg-side.
Hinds tried to swing it away behind square, and he was adjudged caught behind by umpire Simon Taufel, although television replays seemed to suggest that Hinds did not make any contact.
Hinds unfortunately may face ICC Match Referee Chris Broad following the game for standing his ground.
The tourists also benefitted when umpire Billy Bowden adjudged West Indies vice-captain Ramnaresh Sarwan LBW to Thilan Thushara for a well-played 72, but replays again showed that Thushara had run wide on the crease and his delivery appeared to be heading down the leg-side.
"It was tough coming out on the losing side again, but the guys really fought well to try and save the match," Gayle said.
"We have to give them credit for this, since the conditions were tailor-made for the Sri Lankans, but there are a few positive that we can take away from this game."
The second and final Test of the series begins on April 3 at Port of Spain.