West Indies, set 153 to win, reached their target before lunch when Shane Dowrich struck Mohammad Amir for four to reach 154 for 5.
Opener Kraigg Brathwaite, who carried his bat through the first innings with 142 not out, capped a memorable match by finishing with an unbeaten 60 as West Indies secured victory without further loss after resuming at 114 for 5.
Dowrich also scored 60 not out as he and Brathwaite added an unbroken 87 runs for the sixth wicket.
Pakistan won the three-match series 2-1 after winning the first Test in Dubai by 56 runs in Dubai and the second by 133 runs in Abu Dhabi. – AFP