Pakistan, chasing 277, were 256-8 with two overs left when the umpires decided that the light was too poor to continue.
Shoaib Malik, who was 96 not out, was furious with the decision.
Monday's series decider is at the same venue. Zimbabwe's last ODI series win was against Bangladesh in May 2013.
Zimbabwe beat Pakistan by five runs on the Duckworth-Lewis method after a controversial end to the second one-day international in Harare.