Electing to bat at the MCG, Sri Lanka just lost opener Lahiru Thirimanne's (52) wicket on 122 before a 210-run unbeaten second wicket stand between Dilshan (161) and Sangakkara (105) took the Islanders to a commanding total.
Lanka, though, had an edgy start after Thirimanne was dropped off the fourth ball of the innings when Mohammad Anamul Haque Bijoy spilled a sitter at first slip to leave pace spearhead and captain Mashrafe Mortaza disappointed.
The left-handed Thirimanne continued to live dangerously after surviving another half chance off Mortaza but somehow managed to register his 12th ODI half-century in 78 deliveries, his innings laced with three boundaries.
Sharing the new ball with Mortaza, medium-pacer Hossain finally scalped Thirimanne in the 25th over only to see a rough outing on the field.
The veteran Sangakkara, playing his 400th ODI, joined Dilshan at the crease and the duo soon found their groove even as Mortaza kept shuffling his bowlers.
Dilshan, who registered his 21st ODI hundred en route to his 146-ball knock hit 22 boundaries but not a single six - a record.
Sangakkara was also in the attack mode as the left-hander scored 13 fours and a six in his 76-ball stay at the crease.
The left-right batting combination proved deadly for the Tigers, who had no answers to the onslaught.
If the duo changed gears in the powerplays then they cut loose in the final five overs to fetch 58 runs.
Sangakkara though was dropped twice during his stay, once on 23 off Taskin Ahmed in the 33rd over and then off Hossain in the 41st over as the Bangla fielding told a sorry tale.
Making full use of the lives, Sangakkara soon stepped out to the far-from-convincing Bangladesh bowling inthe final ten overs to pulverise the attack.
The wicketkeeper-batsman not only registered his 22nd ODI ton but also his fastest - off 73 balls.
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