Pakistan suffered another dramatic collapse as they lost their last six wickets for a paltry 17 runs with Muthusamy taking 5-57.
In their first innings of 378 they lost their last five wickets for 16 runs. It was a day for the spinners to savour as Noman took 6-112 in 35 overs in South Africa's opening innings, adding two wickets on day three as he applied the pressure from early while spin partner Sajid Khan returned figures of 3-98 in a strong supporting role.
Pakistan lost Imam ul Haq in the second over of their second innings as he came storming down the wicket to spinner Simon Harmer, missed and was easily stumped.
But they had increased their lead to 145 runs at lunch before Abdullah Shafique was caught and bowled by Muthusamy for 41 and the dangerous Babar Azam dismissed for 42.
Kagiso Rabada, who produced a fiery spell in a rare cameo from a quick bowler, was rewarded with Babar's wicket, trapping him leg before wicket in the middle session.
After tea, Muthusamy and Harmer (4-51) romped through the batting order. Muthusamy's 11-wicket haul in the match was the fourth best return by a South African spinner in a Test.
The two sides play a second test, starting on Monday, in Rawalpindi.
