Kumar Sangakkara (56) and Chamara Silva (52) also hit half-centuries and skipper Mahela Jayawardene contributed 46 in Sri Lanka's 318 for four in 50 overs.
Bangladesh were bowled out for 112, leaving their qualification for the next round riding as much on the Sri Lanka versus India match today as on their final match against Bermuda today.
"We're happy with what we've achieved today, but we cannot relax," Jayawardene said. "I see a big game against India on Friday -- we want to win this one, too."
Bangladesh captain Habibul Bashar said Jayasuriya was outstanding, but his lineup let itself down.
"We didn't bowl well today. Our fielding fell short of the mark -- and we need to field really well against the big teams," he said. "It was a bad game for us -- we fielded badly, we lost early wickets, nothing went right."
RSS