Openers Mukhtar Ahmed (83) and Ahmed Shehzad (55) added 142 runs before captain Shahid Afridi hit a boundary off the first ball he faced to seal an emotional victory with three balls to spare.
Earlier, Hamilton Masakadza (43) shone upfront and captain Elton Chigumbura (54) provided the late assault to help Zimbabwe post a strong 172-6 having opting to bat first.
Six years after an attack on Sri Lanka's team bus in Lahore left six Pakistani policemen and a van driver dead, Zimbabwe became the first test-playing nation to tour the country for a limited overs series.
The visitors got off to a strong start with Masakadza and Vusi Sibanda adding 58 runs before Mohammad Sami (3-36), returning to the national side after a three-year absence, dismissed the openers in successive deliveries in the seventh over.
Zimbabwe overcame mid-innings wobbles to reach 114-4 after 15 overs before Chigumbura, beneficiary of a missed stumping opportunity, accelerated hitting Wahab Riaz for three successive boundaries.
The Zimbabwe skipper reached his fifty with an effortless flick that cleared long leg ropes for the only six of his breezy 35-ball knock.

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