Wits piled on the pressure, especially in the second half, striking the woodwork and forcing a number of fine saves from the Smouha keeper.
Phakamani Mahlambi, who came in off the bench, Vincent Pule and Gabadinho Mhango had the best of the opportunities for Wits.
Gavin Hunt’s side now face a difficult away day in the second leg in the Egyptian resort of Borg El Arab on Saturday next week.
Wits: Josephs, Gaxa, Khumalo, Ntshangase, Frosler, Motshwari, Monare, Pelembe (Myeni 61’), Pule, Mhango (Rodgers 74’), Malajila (Mahlambi 60’)