Wasim's spin assault routed the West Indies for a low score of 115 in 19.5 overs which Pakistan surpassed in 14.2 overs to take a 1-0 lead in the three-match series.
Dwayne Bravo hit a gritty half-century to avoid a total disaster, adding a new world record Twenty20 stand of 66 runs for the ninth wicket with Jerome Taylor who made 21.
Pakistan had lost opener Sharjeel Khan for 22 in the fourth over but Babar Zaman (55 not out) and Khalid Latif (34 not out) ensured the target was chased down comfortably.
Earlier, Bravo scored a 54-ball 55 for his fourth half-century and lifted the world champions from a precarious 48-8 in 11.3 overs before being bowled off the penultimate ball.
Wasim made his career milestone in his four destructive overs -- the third best figures for Pakistan in all Twenty20 cricket -- after Sarfraz Ahmed won the toss and opted to bowl on a slow turner at Dubai stadium.
Bravo smashed paceman Wahab Riaz for a six to reach his half-century and led the recovery from a poor start which saw the West Indies struggling at 46-5 in the first ten overs, in danger of falling for under a 100 total.
Wasim then chipped in with wickets of Andre Fletcher (two) and Marlon Samuels (four) in the third over to leave the world champions tottering at 15 for three.
West Indies lost Johnson Charles (seven) and debutant Nicholas Pooran (five) in the next two overs make it 22 for five.
Bravo and Kieron Pollard (nine) took the score to 47 before Wasim struck twice to improve his previous best of four for 11 he took against Zimbabwe at Harare last year.
Taylor and Bravo fell in the final over by paceman Tanvir who finished with 2-26.
The victory gave Pakistan's new T20 captain Sarfraz Ahmed two in two after taking over in his team's nine wicket win over England at Manchester earlier this month.
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