Pakistan restricted Bangladesh to 124-9 in 20 overs after scoring mere 135-8 in 20 overs.
Shamim Hossain scored 30 off 25 balls in Bangladesh's failed run-chase, which was derailed right from the beginning.
Pakistan held their nerves in the crunch situation, courtesy Shaheen Afridi (3/17) and Haris Rauf (3/33).
Earlier, wicketkeeper-batter Mohammad's 31 and Mohammad Nawaz's 25 helped Pakistan to crawl to the total they could manage to put up.
The final match would be Pakistan's third meeting with India in the ongoing Asia Cup amid the bitter tussle in the backdrop of the diplomatic tension over the April 22 Pahalgam terror attack.
In the two matches where they met so far, India have convincingly outplayed Pakistan.
Both the matches were embroiled in controversy as the Indian players- led by skipper Suryakumar Yadav- refused to shake their hands with the Pakistani counterparts.