All-rounder shared in a superb unbroken 132-run partnership with Jason Holder (58*) as hosts finished at 286/6 after Pakistan took early wickets.
The home side failed to put up a fight on Day 5 and only posted a target of 32 which the tourists chased down despite a few hiccups.
The Pakistan captain made 99* while Yasir Shah took 4/33 as West Indies finished the day at 93/4, 28 runs behind.
Pakistan finished the day at 201/4, 85 runs in arrears after West Indies put up a first innings total of 286.
Just 11.3 overs were bowled on Day 2 as West Indies finished at 278/9 with captain Holder fighting on at 55*.
The hosts finished at 244/7 after 63 by Roston Chase and 56 from Shane Dowrich - three wickets for Mohammad Amir and two for Yasir Shah.
Writing in his exclusive blog for PakPassion.net, the renowned West Indies cricket commentator looks forward to the upcoming Test series between West Indies and Pakistan and wonders if the visitors have the resolve and the resources to complete a first ever Test victory in the Caribbean.
Mohammad Hafeez hit 80 while Shoaib Malik made an unbeaten hundred as visitors easily chased down target of 234.
The former hit an unbeaten 125 to guide Pakistan to 282/5 while the latter took 5/38 as the visitors sealed a 74-run victory.