The home side will also be without Thulani Hlatshwayo for their next game after he was sent off five minutes from time.
Both Wits’ goals came in the second half, Sibusiso Vilakazi scoring 10 minutes after the re-start, with Asive Langwe adding the second 10 minutes from time.
Following the kick-off, there were a couple of chances for both sides as Granwald Scott had his header saved by Wits keeper Emille Baron, while Mzikayise Mashaba curled a free kick wide of the target.
The game remained open, play moving from end to end with both sides having their moments of ascendancy, yet struggling to penetrate each other’s defences.
The Clever Boys had a couple more half chances midway through the stanza, but Papy Faty went wide of goal from the edge of the area, while striker Ryan Chapman saw his powerful shot missing at the near post.
The Cape side were again to threaten Wits’ goal during the closing stages of the half, but Mabhuti Khenyeza failed to test Baron with a header from some distance, while Abia Nale went close with a shot from inside the box, but could perhaps have scored if he had found better contact.
The deadlock was broken 10 minutes after the restart, Vilakazi netting from six-yards out after Ajax had gone close through Manyama a few moments earlier.
Wits were able to ensure the home side were not handed any decent chances to come back into the game and then went on to add a second goal in the 81st minute, Asive Langwe getting on the score-sheet with a headed effort following Faty’s delivery from out wide.
Thulani Hlatshwayo’s 85th minute sending off for a second yellow card then served only to rub the salt even deeper into Ajax’s wounds, the Cape Town team ending the day in 15th spot and in the drop zone along with neighbours Chippa United.