Malik capped his one-day return after two years with a fiery 76-ball 112 with 12 fours and two sixes after openers Mohammad Hafeez (86) and Azhar Ali (79) put on 170 for the first wicket.
Haris Sohail made 89 after Pakistan won the toss and elected to bat.
For Zimbabwe Prosper Utseya took 2-63.
The next two matches will be played on Friday and Sunday -- also in Lahore.