Pakistan needed 88 runs to win the first Test after South Africa were dismissed for 245 in their second innings on the fourth day in Karachi on Friday.
Left-arm spinner Nauman Ali took 5-35 while Yasir Shah finished with 4-79 after South Africa resumed at 187-4. Temba Bavuma was the last man out for 40.
The second Test starts on February 4 in Rawalpindi.