Opener Imam-u-Haq hit a sure-footed 128, lifting Pakistan to 308-7.
Asif Ali, making his one-day international debut for Pakistan , blasted 46 off 25 balls in a typical cameo act, while in-form Fakhar Zaman scored 60 off 70 balls.
Babar Azam, returning from an injury, contributed 30 off 34 balls.
Pakistan are starting the series as clear favourites, but captain Sarfraz Ahmed expects the hosts to be challenging opponents in their home conditions as their tour moved to Bulawayo for five games in the longer of cricket´s two short formats.
"The one-day series is important, and it´s not easy to play Zimbabwe in their home conditions," said Sarfraz.
Pakistan : Fakhar Zaman, Imam-ul-Haq, Babar Azam, Shoaib Malik, Sarfraz Ahmed (c&wk), Asif Ali, Faheem Ashraf, Shadab Khan, Hasan Ali, Mohammad Amir, Usman Khan
Zimbabwe : Chibhabha, Chari, Hamilton Masakadza (capt), Musakanda, PJ Moor, Murray(wk), Tiripano, Roche, Wellington Masakadza, Chatara, Muzarabani