Chasing 236 for victory from their allocation of 50 overs, West Indies entered the final overat Queen's Park Oval needing 13 runs to win.
Sri Lanka turned to Vaas, their most experienced bowler, to deliver the last over, and he restricted the West Indies last wicket pair of Chanderpaul and batting bunny Fidel Edwards to three runs from the first four balls of the over.
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But Vaas, whose line and length had been unerring throughout the match, delivered a full length delivery and Chanderpaul drove him through mid-off for four.
Sri Lanka would still have favoured their chances with West Indies needing a six off the last ball when Vaas ran up and delivered a full toss which Chanderpaul duly dispatched over the wide long-on boundary to spark massive celebrations in the stands.
Chanderpaul was undefeated on 62 from 63 balls which included five fours and one six.
The victory gives West Indies a 1-0 lead in the three-Test series which continues at the same venue on Saturday before end