Chibhabha's steady innings propelled the home side to 276 for six in their 50 overs after being sent in to bat.
Pakistan collapsed to 76 for six in their reply, before rallying in the second half of their innings on the back of an excellent 96 not out from experienced batsman Shoaib Malik to leave them with 21 to get from the final two overs.
But with darkness descending on Harare, home umpire Jeremiah Matibiri and Ruchira Palliyaguruge from Sri Lanka pulled the players from the field and revised the Pakistan target to 262, leaving Zimbabwe victorious with the visitors stranded on 256 for eight in 48 overs.
Chibhabha, who was out for 99 when Zimbabwe toured Pakistan in May, looked as though he would score his maiden ODI ton before poor footwork saw him flash at a wide delivery from seamer Wahab Riaz and offer a low catch to wicketkeeper Sarfraz Ahmed.
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It was one of four wickets in the innings for Riaz, who also had home skipper Elton Chigumbura out hit wicket for a well-played 67 from 55 balls.
Standing back in the crease, Chigumbura attempted to smash a low full toss, but succeeded only in crashing his bat into the wickets as he played the shot.
Riaz finished with figures of four for 63 in his 10 overs. Pakistan made a disastrous start to their reply as Zimbabwe seamer Tinashe Panyangara dismissed both openers cheaply on his way to figures of two for 44 in nine overs.
But the tourist mounted a superb rearguard action when Malik and Aamer Yamin (62 from 68 balls) put on 111 for the seventh wicket.
Malik, who was four runs short of becoming the first ever Pakistan number five to score a century in a chase, added a further 63 with Yasir Shah (32 not out) for the ninth wicket before the light intervened and halted their charge.
The series decider will be played at the same venue on Monday.
(Reporting by Nick Said; editing by Martyn Herman)
