Buhle Mkhwanazi, Thabang Monare, Deon Hotto and Mxolisi Machupu who missed the reverse fixture in Dobsonville made a welcome return for the Clever Boys.
With no wins from three matches prior in the group, Wits dropped to the bottom of the mini-table following the goalless draw a fortnight ago in Soweto.
Terrence Dzvukamanja missed a big chance to give Wits the lead on nine minutes when he volleyed a loose ball in the area from a free-kick over the top.
Dzvukamanja fluffed another clear opening nine minutes later with a tame shot on the turn after holding off a challenge, as Brandon Peterson denied Muetaz Husayn at the other end.
Bengazi changed tact straight after halftime as Abdulsalam Mustafa made way for Ahmed Amhimmid. Six minutes later as Bengazi went ahead through an own-goal from Dzvukamanja who tried to clear his defensive lines.
Wits were further behind when Muhanad Alaeeli got behind Zitha Macheke on 61 minutes to head into the near post following a flick on in the area.
The South African side looked to draw inspiration from the bench and introduced Haashim Domingo, who netted the consolation in the final 15 minutes following poor defending.
Wits pushed for an equaliser as the clock wind down, however their wish didn't materialise as the Libyans bagged their first win in the group.