There was a 10 minute delay to the kick-off following the late arrival of fans, but they were greeted by immediate action as Parker put Amakhosi in front.
At the other end, Sibusiso Vilakazi did well to gather the ball from a Chiefs player, before crossing to Sifiso Vilkazi who found the back of the net.
Chiefs applied all the early pressure as they continued to push the Clever Boys' back, and Parker had a header on goal, but it was no trouble for Emille Baron.
In the 25th minute George Lebese took a shot at goal with his weaker right foot, but Baron was again up to the task; while two minutes later Daylon Appolis was brought on to replace Masibusane Zongo owing to injury.
On the half hour mark Chiefs were guilty of some sloppy defending, and and open Vilakazi has a chance, but shot poorly.
Minutes before the hour mark, Patrick Phungwayo worked some magic on the flank to get a cross into the box, but the ball flew over the heads of his teammates.
Keegan Ritchie then created the first effort for Chiefs in the second half as he unleashed a long range shot that went high.
Wits won a number of corners in the second half, but were not able to turn them into anything.
Despite four minutes of added time, the match ended a stalemate.