The Clever Boys fought hard to get a result in Tanzania, however, goals from Jabulani Shongwe, Abednigo Mosiatlhaga and Henrico Botes were not enough to overturn a 3-0 first leg deficit.
The hosts opened the scoring through Ivorian striker Kipre Tchetche before John Bocco doubled their lead.
Shongwe managed to pull one back for Gavin Hunt's side just before the break as the two sides went into the interval at 2-1.
Tchetche then added a third for Azam, before Mosiatlhaga pulled another one back for Wits midway through the second stanza.
Tchetche then completed his hat-trick, and substitute Botes got on the scoresheet with just two minutes left on the clock as Wits succumbed to a 7-3 aggregate defeat.
Hunt made four changes to the side that featured in their 3-0 defeat at home, as Wangu Gome, Liam Jordan, Paseka Sekese and Somila Ntsundwana came in for Tebogo Moerane, Dillon Sheppard, Ben Motshwari and Joaquim Lupeta.
Wits XI: Barr, Bhasera, Lecki, Khumalo, Nhlapo, Gome, Sekese, Jordan, Pule, Mosiatlhaga, Ntsundwana.