Azam, who opened the batting chasing 157 to win, scored his runs off 55 deliveries and hit nine fours and a six.
He shared a decisive partnership with Mohammed Hafeez (36 off 32) as Pakistan cruised to a six-wicket victory.
Zimbabwe would have been bitterly disappointed with their batting effort on a tame wicket.
Only 20-year-old Wesley Madhevere was impressive, scoring 70 off 48 deliveries. Three batters got into the 20s and perished, which ultimately cost the Zimbabweans.