The home side fought back from 27-4 in its first innings at Karachi to beat the Proteas by seven wickets and take a 1-0 lead the two-match series.
Pakistan are currently engaged in a two-Test series against the Quinton de Kock-led side, winning the first match by seven wickets at the National Stadium here on Friday.
Spinners Nauman Ali and Yasir Shah bamboozled the South African batsmen to help Pakistan win the series opener by seven wickets inside four days.
Nauman plucked five while Yasir Shah bagged four to bundle out South Africa for just 245 in the second innings.
Nauman became the oldest Pakistani spinner to take a five-wicket haul in an innings on Test debut.
Aiden Markram and Rassie van der Dussen led South Africa's resistance in overturning a 158-run first-innings deficit.
The 25-year-old has taken just 44 matches to achieve the scalp 200 Test wickets, making him the fastest Proteas bowler to reach the milestone.
The 35-year-old Alam hit nine fours and two sixes in a patient 109 off 245 balls, compiled in just under six hours, to help his team reach 308-8 at stumps.
Fawad's century, also his first on home soil, single-handedly guided Pakistan past South Africa's first-innings total of 220, after the top order collapsed in the final session of the opening day.
Pakistan was reduced to 33-4 at stumps on a pitch devoid of grass as 14 wickets fell on an eventful opening day of the two-test series.
Pakistan's Mohammad Rizwan pulled off a stunner to dismiss South African batsman Rassie van der Dussen during the opening Test in Karachi
Azam has recovered from a thumb injury that kept him out of the two-test series in New Zealand, which Pakistan lost 2-0.
After the second Test which will be played in Rawalpindi from February 4-8, the two teams will compete in three T20 Internationals in Lahore on February 11, 13 and 14.
Faf du Plessis is in Pakistan where South Africa are scheduled to play two Test matches. The first Test will start on January 26 in Karachi while the second will be played from February 4 in Rawalpindi.
The 36-year-old du Plessis is expected to form the nucleus of the Proteas batting in the upcoming two-test series which will be first for South Africa in Pakistan in over 13 years.
South Africa will now play two Tests against Pakistan at Karachi (January 26-30) and Rawalpindi (February 4-8), followed by a three-match T20I series at Lahore, beginning from February 11.
The left-arm pacer, who blamed the current dispensation at PCB for his shock retirement, said he would be available to play for Pakistan again only once the support staff led by head coach Misbah-ul-Haq exits.
Back from New Zealand after a disappointing tour which ended with a 0-2 loss in the two-Test series, Pakistan will now play two Tests against South Africa
The Proteas last toured Pakistan in late 2007 when it won the two-test series 1-0.
The first Test will be played from January 26 to 30 in Karachi while the second will be held in Rawalpindi from February 4 to 8.
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