Pakistan beat South Africa by 93 runs in the first Test in Lahore on Wednesday to take a 1-0 lead in the two-match series.
South Africa, set a daunting 277-run target for victory, were bowled out for 183 on the fourth day at Gaddafi Stadium.
Noman broke a stubborn 73-run stand between Dewald Brevis and Ryan Rickelton to push Pakistan four wickets from victory.
Brevis was taking the fight to the Pakistan spinners and had reached an aggressive career-best 54, with six fours and two sixes, when Noman bowled him with a sharply turning delivery.
After opener Rickleton’s dogged resistance was broken by spinner Sajid Khan just before lunch for a gritty 45, South Africa reached the break teetering at 137-6, still needing 140 more runs for victory.
Kyle Verreynne and Senuran Muthusamy were both on three not out. Noman had figures of 4-69.
Pakistan struck in the first over of the day through fast bowler Shaheen Shah Afridi who trapped Tony de Zorzi for 16 without any addition to the overnight total of 51-2.
Tristan Stubbs struggled to cope with the sharp turn and was on two when a premeditated reverse sweep off Noman safely landed in Salman Agha’s hands.
Brevis reached his second Test half-century with a six off Noman before becoming the spinner’s fourth victim.