The Aces defence were caught napping twice in the opening 15 minutes, and Ngcobo took advantage.
He charged onto a long ball from Calvin Kadi early in the encounter and flicked it over the head of Aces shot stopper Bafana Nhlapo to put the visitors in front.
Six minutes later he received another long pass, this time from Jabulani Shongwe, and again stunned the Aces fullbacks, beating Nhlapo with a thunderous strike.
The home side pulled one back with four minutes left in the opening stanza when Abia Nale provided a neat chip to Tendai Ndoro, who netted a close-range header.
Amazayoni were far more aggressive in the second half, surging forward in search of the equaliser.
Mbulelo Mabizela nearly levelled the scores on the hour mark, climbing high to connect with a corner, but his attempt floated wide to the left.
And Wits keeper Moeneeb Josephs did well to save a double strike from the dominant Aces forwards with less than 20 minutes remaining.
Josephs was again called to action in second-half injury time when he pulled off a stunning save, diving his left to deny a piledriver from Nigerian international Onyekachi Okonkwo.
Despite the home side’s intent, the Clever Boys held firm at the back to cement themselves in third place in the top-flight standings, as they handed Aces their first defeat in seven league matches.