Chasing a target of 264, Salman Agha struck 62 while Mohammad Rizwan scored 55 but Pakistan collapsed from 196-3 to 252-7 before sneaking over the line at the death.
It was seam-bowling duo Lungi Ngidi and Corbin Bosch that sparked a Proteas comeback in the middle overs with the former taking 2-46 while the latter finishing with figures of 2-32.
It was left to home captain Shaheen Afridi, batting at number 9, and number 10 to make sure the hosts go 1-0 in the three-match series.
Earlier, the Proteas would have been disappointed after being bowled out for a total of 263 in 49.1 overs.
That was after Quinton de Kock and debutant Lhuan-dre Pretorius put on 98 for the opening partnership in 16 overs.
Pretorius struck seven fours and a six while scoring 57 off 60 balls while De Kock hit 63 from 71 deliveries in his first ODI appearance in almost two years after reversing his international retirement.
The visitors lost their way in the middle overs with stand-in skipper Matthew Breetzke hitting 42 while another ODI debutant Sinethemba Qeshile scored 22.
Pakistan fought back through spinner Abrar Ahmed (3-53) while fast bowler took 3-40 in 9.1 overs.
The second ODI of the three-match series takes place at the same venue on Thursday.
Dewald Brevis has been ruled out of the Proteas' three-match ODI series in Pakistan, that starts in Faisalabad on Tuesday, after suffering a low-grade shoulder muscle strain.
Pakistan cruised to a four-wicket victory against South Africa in the third T20 International at the Gaddafi Stadium on Saturday to claim the series 2-1.
Pakistan blew the Proteas away with the ball as they cruised to a nine-wicket victory in the second T20I in Lahore on Friday night.
Proteas batter David Bedingham has been ruled out for at least the next month after suffering a quadriceps muscle injury.
