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.
Pakistan looked in a hurry to wrap up the chase with Ahmed hitting Chris Mpofu for four successive boundaries in the bowler's first over.
Brian Vitori was hit for three consecutive fours in the next over as the 22-year-old Ahmed, playing only his second Twenty20 International, cruised to his maiden fifty in 27 balls and Pakistan reached the 100-mark in the 10th over.
At 142 for no loss in the 14th over, Pakistan were cruising to victory before losing five quick wickets as Zimbabwe bowled with considerable discipline to leave the hosts needing four runs from the final four deliveries.
Afridi looked unperturbed by the pressure to nonchalantly dispatch Tinashe Panyangara's third delivery for a boundary to seal victory.
The teams return to the stadium for the second and final Twenty20 International on Sunday before three one-dayers at the same venue.
(Reporting by Amlan Chakraborty in New Delhi; Editing by Tom Hayward)
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