Brandon Peterson, Solly Khunyedi, Haashim Domingo and Phathutshedzo Nange were given starts by Gavin Hunt from the side that overcame Cape Town City in the Absa Premiership a week ago.
Keegan Ritchie, also given a rare run out by Hunt, went close to giving the hosts the lead with a free-kick outside the box on 10 minutes but the effort agonisingly flew over the top.
Wits continued giving the visitors headaches towards the half-hour mark, but the Libyans couldn't crack despite the best efforts of Khunyedi and Gift Motupa amongst others.
Hunt, who remarkably led is charges to a first-ever group stage participation, anxiously watched from the touchline as his front men led by top-scorer Motupa continued firing blanks.
Thus, Hunt had seen enough and introduced Mxolisi Machupu for Motupa as well as Thabang Monare who came on for Domingo following the 68th minute.
In this the first-ever clash between the South African and Libyan sides, Wits almost profited from a counte-rattack but Bengazi pulled back and cleared their lines.
The encounter therefore ended in a stalemate, with the Clever Boys still awaiting their first goal in the group stages.