Pakistan were 217 for eight at lunch, 47 runs short of their target of 264, with two wickets remaining. Misbah was unbeaten on 58.
Fast bowler Tendai Chatara led Zimbabwe's push for a rare win against a leading Test nation, taking two wickets during the morning to add to the two he took on Friday. He had figures of four for 48.
Resuming at 158 for five, Pakistan suffered an early blow when Chatara trapped Adnan Akmal leg before wicket with only five runs added. Akmal, who made 20, went back to a ball which angled in towards his stumps.
Abdur Rehman scored 16 in a seventh wicket partnership of 34 with Misbah, who was content to continue to bat watchfully, as he had done on the fourth afternoon, before Rehman was caught behind off Tinashe Panyangara.
Chatara returned to the attack and immediately claimed the wicket of Saeed Ajmal in almost identical fashion to the way he dismissed Akmal, with the batsmen going back to a ball which cut back sharply and hit him on the pads.