The result drops Ajax into the bottom three on the log, with just nine points from 11 matches – they have been overtaken by neighbours Chippa United. The Clever Boys remain firmly in sixth position with 16 points.
Wits had the first chance on goal when Calvin Kadi had a shot saved by Sander Westerveld, and on 25 minutes Kadi came close again with a header, after Ajax's backline were lax in closing him down.
Two minutes later Khama Billiat had a chance for the visitors from 25 metres, but his attempt was saved by Ryan Harrison.
The first half was low on clear-cut chances and the teams headed into the break with the score at 0-0.
On the hour mark, a shot by Faty Papy swerved just over Westerveld's goal area, and two minutes later Thulani Hlatshwayo came close to giving his side the lead, when he rose unmarked at the far post and hit the upright with a header, with the keeper well beaten.
The Urban Warriors were denied a winner nine minutes from time when Billiat's goal was called offside.