Tashreeq Morris gave Ajax the lead, tucking home from close range after Nathan Paulse helped-on the impressive Riyaad Norodien's cross from the right flank. Norodien was playing only his second game for the Urban Warriors.
After that goal Wits fought back and hit the woodwork twice through Sibusiso Vilakazi and Buhle Mkhwanazi, while Sameegh Doutie missed two great chances. Siyabonga Nhlapho missed an even better one inside the box when he shot over the bar, and Anssi Jaakkola had to make an important save one-on-one against Vilakazi to keep his side one up.
Moeneeb Josephs was also in good form at the other end, saving in a one-on-one situation to deny Morris his second of the night. The first half ended 1-0 to the home side.
The second half started out much the same as the end of the first, with Wits pushing hard for an equaliser. Gradually the game became more open as Wits left holes at the back by pushing forward more and more.
The Clever Boys missed a host of chances to score and will be kicking themselves at the result, as they were certainly not outplayed by any stretch despite the flattering scoreline for Ajax.
In fact, Wits hit the woodwork three times in the match, twice in the first half and again in the 83rd minute when Ben Motshwari's first-time strike cannoned back off Jaakkola's right-hand upright. Just before that the creative Shongwe played in Fikru Tefera Lemessa one-on-one but Jaakkola came out and made himself big, forcing the striker to put it over the bar.
Then Wits were dealt a sucker-punch on the counter-attack in stoppage time as Keagan Dolly's pinpoint cross from the left found Bantu Mzwakali unmarked in the area, and all he had to do was nod it past a helpless Josephs, who could do nothing about it.
Thulani Hlatshwayo pulled one back immediately for Wits with a brilliant bicycle-kick finish from the penalty spot after Motshwari won a header outside the box, but it was too little too late.
Roger de Sa's side are the first in the hat for the Nedbank Cup semi-final draw. Man of the Match was young midfielder Norodien.