Jayasuriya, 37, scored 115 from 101 balls after his team lost the toss and were put into bat on a slow wicket in overcast conditions at the Providence Stadium in Guyana.
It was his 25th one-day century as he helped Sri Lanka rack up 303-5 in the second-phase game.
West Indies were never in the hunt and were bowled out for 190 as Sri Lanka won by 113 runs. West Indies are now relying on other results going their way but Sri Lanka's destiny is in their own hands.
Left-arm spinner Jayasuriya, who helped his team recover from early difficulty at 35 for two, was the clear man of the match as he also collected three for 38 with the ball.
'BEST KNOCKS'
"That was one of the best knocks I've played because it was not a very easy wicket to bat on and also we didn't want to lose any wickets so we were a little under pressure," Jayasuriya told reporters.
Jayasuriya showed no signs of age 11 years after he was voted man of the tournament when Sri Lanka won the 1996 World Cup.
The left-hander, who said he wanted to finish the World Cup "on a very good note" before deciding on his future, still appears to have the same drive and passion for his game now as he always has.
Certainly his skipper Mahela Jayawardene, who scored 82 in the match and put on 183 with Jayasuriya, is grateful to have him around still.
"I've seen quite a lot of him to be honest and I would probably rank this (innings) as one of his top ones," Jayawardene said.
"He's a big game player, he's done it not just against small teams in low-key tournaments, but he has done it in big tournaments under pressure. That's why he is something different."
West Indies captain Brian Lara was full of admiration for his fellow 37-year-old and was in no doubt that Jayasuriya -- described by commentator Barry Richards as a "pocket rocket" -- changed the course of the match.
"He was exceptional," Lara said. "We did not see it coming as after 15 overs there were 50 runs on the board and two wickets. You would think that if we kept the pressure on they would try to build their innings slowly.
"But their next five overs went in excess of 50 runs and set the tone for the innings. He played to his strengths and took on the short boundary.
"All credit must be given to him. He's in his 38th year and still looks capable of doing the job."
The seven-week tournament, the first to be played in the Caribbean, culminates in the final in Barbados on April 28.
