The 30-year-old left-hander notched 101 for his seventh one-day hundred to propel the defending champions to 357-9 in their 50 overs before restricting Bangladesh to 226-7 in 50 overs.
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Bangladesh were never on target as they lost opener Nazimuddin (one) and captain Mohammad Ashraful (eight) by the 10th over.
Only Mushfiqur Rahim (44) and Raqibul Hasan (35) offered some resistance during their fourth wicket 78-run stand in an otherwise disappointing batting display.
Mashrafe Mortaza (34) and Abdur Razzak (22) added 49 for the unbroken eighth wicket stand but it was too little and too late.
Sri Lanka play United Arab Emirates (UAE) on Thursday to decide who tops the Group. Bangladesh beat UAE by 96 runs on Tuesday.
Pakistan, India and Hong Kong are placed in Group B. The top two teams qualify for the Super League stages in which all teams play each other once to decide July 6 finalists.
Sri Lanka, who won the toss and batted, were indebted to Sangakkara and Sanath Jayasuriya