The hosts finished their 50 overs on 296-9, with Mohammad Hafeez (80) leading their charge, but Zimbabwe’s reply lasted only nine overs – they reached 68 without loss before the weather won out.
As a result of the washout, Pakistan took the series 2-0 ahead of July’s five ODIs against Sri Lanka.
After winning the toss and electing to bat, Azhar Ali’s fine run of form continued as he lay on a good partnership for the first wicket with Hafeez.
The pair passed 100 for the first wicket – the second time they have done so in the series – and looked set to dominate the innings before Hafeez called for an ill-judged run.
Azhar, who hit 102 in the second ODI on Friday, responded but the lack of a dive and a direct hit from Sikandar Raza at cover left him short of his ground four short of his fifty.
Raza was again involved as Hafeez went for a run-a-ball 80, trapped in front by the part-time spin of the Zimbabwe batsman, before he made sure of career-best figures with the removal of Asad Shafiq.
That brought debutant Babar Azam to the crease and, despite losing regular wickets, he moved to an impressive half-century.
Raza, who finished with 3-59, also accounted for Sarfraz Ahmed as a dangerous cameo of 25 ended when he tried to go over the top and could only succeed in finding Sean Williams who took a good, low catch at mid-wicket.
As the innings continued to stutter, Babar passed fifty but, after he was bowled for 54, it was left to Anwar Ali to provide some late impetus and push the score to 296-9 with a 23-ball knock of 38.
Zimbabwe made a strong start in reply, with openers Chamu Chibhabha (39) and Vusi Sibanda (28) steering them to 68 without loss, before a floodlight failure, a dust storm and finally heavy rain led to the match being called off.