Chanderpaul hit the penultimate ball for a straight four and then crashed a full toss from Vaas over the mid-wicket boundary for a remarkable victory.
"We're happy with the win but we would have been happier if we could have sealed the victory if we could have won the game with more wickets in hand," said Dwayne Bravo, West Indies all-rounder.
"We knew that Shiv was there and once he got most of the strike we were in with a chance.
"We knew it would have been difficult with two balls to get 10 runs and with a bowler as experienced as Chaminda Vaas you would back the bowling team but Shiv has done it already on different occasions and it goes to show his experience."
|" ...Shiv has done it already on different occasions and it goes to show his experience."|
West Indies all-rounder
Sri Lanka, who were without key bowlers Lasith Malinga and Muttiah Muralitharan, were struggling at 49 for 5 after Bravo claimed three early wickets, before Chamara Kapugedera (95) and Chamara Silva (67) put on a sixth wicket partnership of 159 to turn the innings around.
"We played a lot of good cricket and a lot of bad cricket but to come back from that situation and make 235 showed the character of the guys," Trevor Bayliss, Sri Lanka coach, said.
Chris Gayle, West Indies captain, began aggressively as he hit eight fours in his 52 before being trapped LBW by debutant spinner Ajantha Mendis with the home side on 109 for 2.
But that was the first of three wickets in seven balls as the in-form Ramnaresh Sarwan was caught behind off Nuwan Kulasekara for 35 and then the out-of-form Marlon Samuels went to the same bowler for a duck, after he was trapped plumb LBW to send the home side into a spin.
Bravo joined Chanderpaul and clubbed two sixes over cover to put West Indies back on track, but he was run out for 36 from 37 balls.
When wicket-keeper Patrick Browne (15) and all-rounder Darren Sammy (1) went, Chanderpaul was running out of partners, and with 17 runs needed from the last two overs, Suliemann Benn played and missed at the first four balls of Nuwan Kulasekara's over and was then run out on the fifth ball.
Chanderpaul hit a four off the last ball of the penultimate over to leave last man Edwards on strike with 13 runs needed from the final six balls.
Edwards scrambled a single off the second ball to give his partner the strike but Chanderpaul could only manage another single himself.
A further single from Edwards left Chanderpaul needing 10 to win from the last two balls and after his textbook drive for four, Vaas delivered a full toss that was dispatched high over Sri Lanka skipper Mahela Jayawardene at mid-wicket for victory.
The two teams meet again at the Oval on Saturday before concluding the series in St. Lucia on Tuesday.