The pair came together with Pakistan slipping at 128 for five after they had been inserted by the Zimbabweans, and each scored half-centuries to take the tourists to a final tally of 259 for six.
Both batsmen ended up scoring at a run a ball on a dry surface, with Rizwan finishing unbeaten on 75 and Wasim run out for 61 in the final over of the innings.
From that point Pakistan slumped to 35 for three after 10 overs as seamers Tinashe Panyangara and Luke Jongwe were rewarded for their persistence with the wickets of Ahmed Shehzad and Mohammad Hafeez respectively.
Sarfaraz Ahmed and Shoaib Malik resurrected the innings as they added 65 for the fourth wicket, only to undo their good work by running down the pitch at Zimbabwe's spinners.
Fortunately for Pakistan they had two middle-order batsmen in good form, with Rizwan and Wasim fresh from good outings in the Twenty20 international series, which the tourists swept 2-0.
They seamlessly restored some stability to the Pakistan innings, before cashing in at the end as they reaped 78 runs from the last eight overs.