It was Sri Lanka's second win in a row after the 16-run defeat of Pakistan in their opening match and helped them step closer to becoming the first team to take a berth in the June 24 final.
Bangladesh, who had lost to India on Wednesday, are virtually out of contention in the four-nation tournament.
Sri Lanka put on a dazzling batting performance to record the highest total ever at the Rangiri international stadium in Dambulla.
Dilshan and Upul Tharanga set the ball rolling with an opening stand of 111 by the 16th over after Sri Lankan captain Kumar Sangakkara won the toss and elected to bat in the day-night match.
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Tharanga (54) and Sangakkara (52) hit half-centuries to build on Dilshan's aggressive knock which included 11 boundaries and a six.
Mahela Jayawardene chipped in with 43 during a third-wicket sta