Pakistan posted 165 for four in their 20 overs after electing to bat first as Usman Khan struck 39 from 30 balls and Tayyab Tahir provided a late boost with 39 not out from 25 deliveries.
Captain Sikandar Raza led the Zimbabwe reply with 39 from 28 balls but they collapsed from 77-2 to 108 all out as the visitors mastered the slow wicket.
The second match of the three-game series will be played at the same venue on Tuesday.