Cosmos were aggressive in the opening stages, but it didn't take long for their former player, Calvin Kadi, to test Ezenkosi.
The Wits striker, who has lost a bit of form lately, shot wide from inside the goal area when he should have done better.
Then Thando Mngomeni missed a clear cut chance, directing Patrick Phungwayo's cross wide of goal.
Sifiso Myeni also went close for Wits, but it just didn't seem to be their day in front of goal.
Fortunately for the embattled Roger De Sa, his rising star goalkeeper Darren Keet was on hand to deny Cosmos' new man Norman Smith a goal on debut.
Sifiso Vilakazi made his Wits debut barely 24 hours since transferring from Ajax Cape Town.