Razzak finished with 4-23 off 10 overs as the tourists were dismissed for 132 in reply to Bangladesh's total of 278-6. He was backed by paceman Mashrafe Mortaza and fellow-spinner Mohammad Rafique, who took two wickets apiece.
It was Bangladesh's eighth successive win in One-day internationals, including a recent 5-0 sweep against Zimbabwe at home.
Opener Fraser Watts top-scored for the tourists with 29. Neil McCallum (23), John Blain (22) and Glenn Rogers (20 not out) were the other main scorers.
Bangladesh were indebted to Aftab Ahmed (52) and lower-order batsman Mortaza (51 not out) for setting a stiff target for the tourists. Mortaza smashed five sixes and two fours in his 28-ball knock.
Seamer Craig Wright and off-spinner Majid Haq each captured two wickets for Scotland, who lost the opening match by six wickets at Chittagong on Friday.
Bangladesh: 278-6 in 50 overs (Aftab Ahmed 52, Mashrafe Mortaza 51 not out, Saqibul Hasan 44, Mohammad Ashraful 38 not out; Craig Wright 2-46, Majid Haq 2-57).
Scotland: 132 in 41.3 overs (Fraser Watts 29, Neil McCallum 23, John Blain 22, Glenn Rogers 20 not out; Abdur Razzak 4-23, Mohammad Rafique 2-23, Mashrafe Mortaza 2-39).