Sahibzada Farhan top-scored with 74 while fellow opener Saim Ayub struck 66 as Pakistan posted a total of 189-4 in their 20 overs after electing to bat first at the toss.
Spinner Roston Chase was the pick of the Windies bowlers with figures of 1-31 in his four overs while seamers Shamar Joseph and Jason Holder took a wicket apiece.
The Caribbean side were well-placed in the run-chased thanks to 60 from opener Alick Athanaze and Sherfane Rutherford, who struck a 35-ball 51.
Pakistan though fought back gallantly and chipped away in the wickets column with left-arm wrist-spinner Sufiyan Muqeem keeping it tight with 1-20 in his four overs.
West Indies were eventually restricted to a total of 176-6 to give Pakistan a 2-1 series win.