It was the fifth-largest win by runs in the history of the game. It was also Sri Lanka's biggest victory in 182 Tests and Bangladesh's worst defeat in 59 matches since gaining Test status in 2000.
Dilshan scored an impressive 143 -- his second century of the match -- as the visitors set an improbable 624-run target for the hosts.
Bangladesh were bundled out for 158 in their second innings on the penultimate day to lose the series 2-0.
Dilshan, who picked 4-10 with his part-time spin, was named both man of the match and of the series.
Middle-order batsman Shakib Al Hasan (46) and wicket-keeper Mushfiqur Rahim (43) were the main scorers in a dismal Bangladeshi batting performance lasting merely 49.
2 overs.
Dilshan was brilliantly backed by unorthodox spinner Ajantha Mendis who picked 3-57 to finish with a match haul of seven wickets.
Mendis started the slide when he took three quick wickets in his opening spell, removing opener Imrul Kayes (five), Junaid Siddique (f