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.
The Proteas fell short in a mammoth run-chase to lose by 30 runs in the fifth and final T20I against India in Ahmedabad as the hosts sealed a 3-1 victory in the five-match series.
The fourth T20I between India and the Proteas was abandoned without a ball being ball after the umpires deemed the excessive fog was dangerous for the players to take field in Lucknow.
Simon Harmer says it is privilege to represent the Proteas after scooping the ICC Player of the Month award for November following his heroics in the historic Test series win in India.
In a tough afternoon for the batters, the Proteas were bowled out for 117 and suffered a seven-wicket defeat to India in the third T20I of their tour to India.
