Pakistan is leading the three-match series by 2-0.
Umer Gul bowled superbly and grabbed four wickets while Mohammad Hafeez and Saeed Ajmal picked up two and one wickets respectively.
From Bangladesh Nasir Hossain made 100 runs while Shakib Al Hasan 34 runs.
Earlier, Pakistani skipper Misbah-ul-Haq won the toss and set 263 runs target for host Bangladesh to win the match.
Middle order batsman Umar Akmal scored highest 59 runs while boom boom Shahid Afridi made 42 runs. Younus khan and Misbah scored 37 runs each while Mohammad Hafeez made 32 runs.
Nasir Hossain of Bangladesh was declared man of the match.
The final one-dayer will be played in Chittagong on Tuesday before the rivals face-off in two Test matches.
Brief scores: Pakistan 262-7 in 50 overs; Bangladesh 186-7 in 50 overs.
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