The left-handed opener scored an 87-ball 109 for his 24th hundred as Sri Lanka posted a challenging 318-4 after being put in to bat on a good pitch at the Queen's Park Oval.
He also became the second-highest century-maker, behind only Indian Sachin Tendulkar who holds the world record with 41 hundreds.
Sri Lanka's total proved too big for Bangladesh, who were bowled out for 112 chasing a rain-revised target off 311 off 46 overs to suffer their first defeat in two matches.
Bangladesh still have a chance to qualify for the Super Eight stage as they meet debutants Bermuda in their last Group B match, while Sri Lanka boosted their hopes with a second successive victory.
Mohammad Ashraful top-scored with an unbeaten 45. Skipper Habibul Bashar (18) and Aftab Ahmed (12) were the others to reach double-figures in a dismal Bangladeshi batting performance.
Bangladesh were rocked by Lasith Malinga, a fast bowler with deceptive round-arm action and a gold-tinted hairdo, who grabbed two wickets in his four incisive opening overs. Malinga eventually finished with three wickets.
Sri Lanka's victory was set up by Jayasuriya who went on the rampage in the morning, smashing seven sixes and as many fours in a magnificent display of aggressive batting.
Sri Lanka's batting flourished, with Kumar Sangakkara (56) and Chamara Silva (52) making their second successive half-centuries and skipper Mahela Jayawardene chipping in 46.
They will now clash with India in their last match here on Friday. India are in a must-win situation after posting just one win in two matches, their victims being Bermuda.
Bangladesh, who had bowled and fielded superbly against India on the way to a shock five-wicket win, failed to repeat their performance against Sri Lanka as they dropped three catches and missed a few run-out chances.
Jayasuriya, who had left the field on 83 due to cramp, returned in the closing overs to complete his hundred in style, with a six off left-arm spinner Abdur Razzak.
The 37-year-old had already put his team on course for a big total before he had retired hurt, dominating the Bangladeshi seamers and spinners with attractive strokes on both sides of the wicket.
Jayawardene, Sangakkara and Silva continued the good work to ensure Bangladesh chased a stiff target in the match which was interrupted twice due to rain.
Bangladesh elected to field after winning the toss, hoping to exploit early moisture on the pitch, but the move failed as Jayasuriya went for big shots early in his innings.
Jayasuriya hit two sixes off seamer Syed Rasel to set the trend and went on to add 98 for the opening wicket with Upul Tharanga (26).
Tharanga survived a run-out chance early in his knock before falling to a brilliant catch at point off left-arm spinner Mohammad Rafique, fielder Ahmed holding the ball on the second attempt.
But there was no respite for Bangladesh as Jayasuriya continued to dominate the attack, hoisting Razzak for two sixes in an over before racing to his half-century off 43 balls.