Haris Raul dented Zimbabwe early after Pakistan chose to bowl.
Usman Qadir bagged three wickets to leave Zimbabwe reeling.
Ryan Burl made 32 to push Zimbabwe's score to 134 for 7.
Fakhar Zaman fell early in the chase.
Babar Azam (51) and Haider Ali (66*) scored 100 for the second wicket to seal a Pakistan win in 15.1 overs. They also bagged the three-match series 2-0.