The visitors did most of the attacking in the opening stages of the game, while Cosmos were happy to sit back and launch counter-attacks.
A good move in the 23rd minute saw Mgakolodi Ngele's cross finding his Wits teammate Cuthbert Malajila, who headed wide of the target.
The Clever Boys were finding it difficult to penetrate the Ezenkosi defence. So they resorted to playing crosses into the Cosmos box for their main striker Malajila.
In the 34th minute, Siboniso Gaxa made an overlapping run, before playing a dangerous low cross which was cleared away by Cosmos defender Shane Thompson.
The Cosmos defence was marshalled by giant centre back Frederic Nsabiyumva, who was showing off his aerial prowess for the home side.
A counter-attack move led by Matsilele Sono saw Linda Mntambo scoring from a rebound on the stroke of halftime and Cosmos were leading 1-0 at the interval.
Wits head coach Gavin Hunt made a double substitution during the break - introducing pacey wingers Phakamani Mahlambi and Daine Klate.
The home side continued to defend too deep as they looked to catch the Clever Boys defence napping again and double their lead.
