Zimbabwe, who were already one wicket down when they resumed on the fifth morning in pursuit of a victory target of 342, slumped to their lowest total against Pakistan in a dismal batting display.
Pace bowler Junaid Khan took two wickets in the first three overs, dismissing captain Hamilton Masakadza caught in the gully for one off a searing delivery and trapping Vusi Sibanda lbw for six.
The spinners then set about securing victory with left-armer Abdur Rehman claiming his first three victims through rash strokes by Malcolm Waller (17), Sikandar Raza (24) and Elton Chigumbura (28).
Ajmal captured two wickets in three balls to finish with four for 23 in the innings and Rehman ended with four for 36.
Zimbabwe proved competitive through the first three days of the test but an unbeaten double century from man-of-the-match Younus Khan took the game away from the home team on Friday.
"For three-and-a-half days we fought hard but then let it get away from us," said Masakadza in the post-match television interviews. "We must focus now on the positives from the game."
Misbah-ul-Haq, the Pakistan captain, added: "We were left behind in the first two days but Younus played a match winning innings. That is what senior players can provide for you."
The second and final Test will also be played at the Harare Sports Club, starting on Tuesday.