The left-handed opener gave a superb exhibition of power-hitting, hammering four sixes and 10 fours in his 101-ball 115 for his 25th century to help his team recover from a shaky start.
Sri Lanka were struggling at 35-2 after being put in to bat in overcast conditions, but were rallied by Jayasuriya who put on 185 for the third wicket with skipper Mahela 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 produced a vital knock under pressure.
The West Indies desperately need a win to sustain their hopes of making it to the semi-finals after losing to defending champions Australia and New Zealand in their opening two games in the second round.
They gave a sizeable home crowd plenty to cheer about early in the innings before being dominated by the 37-year-old Sri Lankan opener.
Jayasuriya was deprived of the strike in the opening 15 overs, but 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.
Sri Lanka managed just 50 runs in the opening 15 overs before plundering 43 in the next five, thanks to Jayasuriya's onslaught.
The West Indies had virtually lost their early advantage after Jayasuriya's amazing blitz. They grabbed two early wickets following impressive spells from their seamers before running into Jayasuriya.
Daren Powell sparked early celebrations in the West Indies camp when he bowled opener Upul Tharana (eight), who was beaten by the movement. Kumar Sangakkara contributed just seven before being caught behind off Bradshaw.
The West Indies bowled well in the opening 15 overs, but were clueless when Jayasuriya went on the rampage. None of their bowlers could put pressure on the Sri Lankan opener, who kept finding gaps in the field.
Jayawardene took time to settle down but did well to keep his end intact. He rotated the strike intelligently, giving Jayasuriya enough chances to step up the run-rate.
The Sri Lankan captain grew in confidence as the innings progressed, hitting one six and two fours in his 113-ball knock.
Fall of wickets: 1-18 (Tharanga), 2-35 (Sangakkara), 3-218 (Jayasuriya); 4-251 (Jayawardene); 5-268 (Silva)
Toss: West Indies
Umpires: Mark Benson (ENG) and Daryl Harper (AUS), TV umpire: Simon Taufel (AUS)
Match referee: Jeff Crowe (NZL)