The visitors passed the target for only the loss of three wickets with 96 balls to spare, with Asad Shafiq (38) and Shoaib Malik (34) unbeaten at the Harare Sports Club.
After Zimbabwe's opening pair amassed 89 runs, the hosts lost 10 wickets for just 72 runs.
Chamu Chibhabha and Richmond Mutumbami set a solid foundation before Chibhabha spooned an easy catch back to the bowler. It sparked a quick slide, even though Asif took some time to get into his stride, taking his first wicket in his fifth over but then proceeding to send the home batsmen back to the pavilion at regular intervals.
Mutumbami was the seventh wicket to fall for a career best 67 but by then Zimbabwe were already in dire straits as the spinners reeked havoc.
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Left-armer Imad Wasim also grabbed three wickets.
Pakistan completed their run chase in 34 overs.
(Reporting by Mark Gleeson, editing by Pritha Sarkar)
