Misbah's 67 was particularly crucial to the Pakistani cause, as he battled through some early challenges before helping to lift his side to a total of 260 for six.
The series decider had been cast into doubt after Zimbabwe's players threatened to boycott the match over unpaid salaries and match fees, but the home side took the field after setting a new ultimatum for the first Test on Tuesday.
For a side with off-field distractions, the Zimbabweans started surprisingly well in the field after Brendan Taylor had won the toss and asked Pakistan to bat on a slow surface.
When Shehzad fell to part-timer Hamilton Masakadza for 54 in the 33rd over, Pakistan had just 119 on the board but Umar Amin lifted the scoring rate with a brisk 33.
Misbah reached fifty from 74 balls before opening up, while Sarfraz Ahmed and the returning Hafeez also weighed in as a late flurry brought 94 runs in the last 10 overs.
