The left-handed opener gave a magnificent display of power-hitting to crack a 101-ball 115 for his 25th century as Sri Lanka posted a challenging 303-5 to leave the hosts to score their highest total batting second.
The West Indies wilted under pressure as they were bowled out for 190 to suffer their third successive defeat in the second round, with Shivnarine Chanderpul top-scoring with an impressive 76 which contained five sixes.
They now have just two points from four matches, thanks to their win over fellow-qualifiers Ireland in a group game. No hosts have ever won the World Cup and the West Indies look unlikely to change the trend.
The West Indies' slim hopes of making it to the last-four now largely depend on other teams' results. They will meet South Africa, England and Bangladesh in their last three games.
The West Indies, whose highest total batting second was 300-3 against South Africa at Centurion in 2004, faced a tall order after losing three wickets for a paltry 42 runs.
"We batted well in the morning," said Sri Lanka skipper Mahela Jayawardene, whose side now have four points from three matches.
"Overall, the stand with Jayasuriya was very good as we managed to step up the run-rate after the opening 15 overs. I just wanted to spend time in the middle and today's outing will definitely help me."
A change in the batting order failed to produce the desired results as the West Indies lost Dwayne Bravo (21), skipper Brian Lara (two) and Chris Gayle (10) in the opening 11 overs.
Lara was undone by a smart piece of stumping by Kumar Sangakkara, standing up to left-arm seamer Chaminda Vaas. The Sri Lankan wicket-keeper brought off another fine stumping, the victim this time being Ramnaresh Sarwan (44).
Sarwan and fellow-Guyanese Chanderpaul defied the Sri Lankan attack, but the asking-rate kept climbing after their team had managed just 100 in the first 30 overs.
The West Indies were yet again let down by batting as they lost their last six wickets for 56 runs, with left-arm spinner Jayasuriya finishing with 3-38.
Pacemen Lasith Malinga and Vaas, and off-spinner Muttiah Muralitharan each took two wickets.
"We have to pick ourselves up in the remaining matches and you never know what can happen in this World Cup. All credit to Jayasuriya and Mahela," said the West Indies captain.
Sri Lanka's total owed much of its substance to Jayasuriya, who surpassed Pakistan's Inzamam-ul-Haq (11,739) to become the second-highest scorer in one-dayers with 11,816. He is behind only India's Sachin Tendulkar (14,847).
Sri Lanka were struggling at 35-2 after being put in to bat, but were rallied by man-of-the-match Jayasuriya who put on 183 for the third wicket with Jayawardene (82).
Jayawardene returned to form just when his side needed runs to boost their chances of qualifying for the semi-finals. He had failed in his last two matches, but played a vital innings under pressure.
Jayasuriya, deprived of the strike in the opening 15 overs, began the fireworks when he hooked left-arm seamer Ian Bradshaw for a four and then lofted him over mid-on for another boundary.
His best came in the next over as he used his feet remarkably well to punish seamer Dwayne Smith, smashing three fours and a straight six. His first 14 runs had come off 33 balls, but the next 27 off just nine.
The West Indies had virtually lost their early advantage after Jayasuriya's amazing blitz. They grabbed two early wickets before being dominated by the Sri Lankan opener.
Jayawardene took time to settle down, but grew in confidence as the innings progressed. He rotated the strike intelligently, giving Jayasuriya enough chances to step up the run-rate.