Sangakkara celebrated becoming only the fourth player to ever appear in 400 one-day internationals by scoring 105 off just 76 balls.
He put on a 210-run partnership with Dilshan ??? who???s own impressive knock came from 146 deliveries with 22 fours ??? as Sri Lanka posted a score of 332-1 from their 50 overs.
Bangladesh were embarrassingly sloppy in the field with a mix of grassed catches, missed run-out opportunities and leaked runs and they didn???t fare much better with the bat, with only Shakib Al Hasan (46) providing any real threat as they fell to 240 all out.
Sri Lanka won the toss and chose to bat on a cracking surface at the MCG but Bangladesh should have made an early breakthrough when Lahiru Thirimanne (52) was dropped in the very first over at slip off Mashrafe Mortaza, with Sri Lanka still to register a run.
It was the first of a catalogue of errors, with wicketkeeper Mushfiqur Rahim in particular having a nightmare outing ??? he failed to go for a catch when Thirimanne edged behind again in the ninth over and missed a stumping opportunity to the same batsman in the 22nd over.
The opener did finally fall three overs later as he smashed a Rubel Hossain (1-62) short ball to the man at third man with the score on 122.
Enter Sangakkara and he continued to pile the misery on the Bangladesh bowlers with 13 fours and a six in his entertaining knock.
He too benefitted from his fair share of fortune though ??? dropped on 23 by Taskin Ahmed, although it was an admittedly difficult caught and bowled chance, and again on 60 off the bowling of Rubel, when shelled at point.
That came shortly after Dilshan had brought up his 21st ODI hundred in the 41st over, and he was given his own reprieve two overs later when Mushfiqur failed to collect the throw at the stumps.
Sangakkara had to wait until the first ball of the last over to bring up his 22nd ODI ton as Sri Lanka set Bangladesh 333 to win.
Their chase started in the worst possible fashion as a trademark Lasith Malinga (3-35) yorker cleaned up Tamim Iqbal for a second-ball duck.
But Anamul Haque (29) and Soumya Sarkar (25) in particular stayed positive and were going along nicely at more than a run-a-ball before the latter departed ??? edging Angelo Mathews through to Sangakkara being the stumps.
Mominul Haque fell for just one to Suranga Lakmal (2-49) the next over and Bangladesh were suddenly reeling at 41-3.
The errors continued when Anamul was run out by Mathews in the 16th over and Mahmudullah fell for 28 soon after.
Shakib rebuilt the innings, slowly, scoring just 18 runs from his first 43 boundary-less deliveries. But with the score at 122-5 at the end of the 28th over and the run-rate required creeping up towards 10 an over, he launched an impressive but brief counter-attack.
In an 18-ball spell 41 runs were added to the score with Shakib hitting four fours and a six and his partner at the crease, Mushfiqur (36), pitching in with one of each.
It looked like they had Sri Lanka temporarily rattled with some sloppiness creeping into their fielding but when Dilshan (2-35) took the key wicket of Shakib in the 32nd over, the game was all but over.
Sabbir Rahman top-scored with 53 but with the required rate now well over 10, he and Musfiqur only crept through the batting powerplay with 22 runs.
Their plan was obviously to see out the 50 overs and improve their net run-rate but Lakmal bowled Mushfiqur two balls later and Dilshan picked up Mortaza for seven before Malinga wrapped things up in the 47th over with the wickets of Rahman and Taskin in consecutive balls.
Sri Lanka next play England in Wellington on Sunday, while Bangladesh are not in action till Wednesday when they face Scotland in Nelson.