The Super Eagles who fired blank in their opening fixture against Rwanda made their intentions known when full back James Daniel's long throw was headed to the path of diminutive Anthony Okpotu who could not connect after just two minutes on the clock.
Nigeria used their aerial presence but winning all second balls with right back James Daniel marauding on the wings with his teasing crosses which caused problems for the Libyan rear.
Salisu Yusuf's charges looked very lively on the counter with winger Chukwudiebube Ogbugh driving through the left and shooting just wide off the Libya far post on 25 minutes.
Stephen Eze tried his luck from a distance twice in succession but on both occasions failed to threaten Libya keeper Mohamed Nashnush two minutes before the break.
Faleye sped past his marker on the left before crossing in the Libya area Ogbugh's diving header on target forced a save from the Libya captain in goal ten minutes after the break.
Substitute Abdelsalam Alaqoub turned midway the Nigeria half and release the cracking right foot shot just wide of Eze goal on 65 minutes.
Unmarked Faleye broke the deadlock on 79 minutes turning in Osas’ corner from close range and secure Nigeria the much needed victory.
Substitute Ibrahim Mustapha missed a good opportunity to increase Nigeria's lead three minutes after the goal when he ran through on goal but his cut back to Faleye was weak allowing a Libya defender to clear the ball to safety.
Equatorial Guinea will take on Rwanda in the late game in Group C in Tangier after they went down 3-0 against Libya.
Total Man of the Match: Stephen Eze (Nigeria)
Omar El Maryami (Head Coach, Libya)
The players were not in shape to express themselves on the field. We tried to put pressure on the Nigerian team but the players could not give what was expected of them. Our goal was to win and to win you have to score goals. We were not good today. It’s football and we have to accept the loss. We have to give our all against Rwanda to win and qualify for the knockout stage to honour our national colours.
Salisu Yusuf (Head Coach, Nigeria)
It was a very difficult victory. We faced a very good team in Libya, who created a lot of problems on the ground. Our opponents were more comfortable than us backed by their victory against Equatorial Guinea in their opening match. We advocated a strategy to close spaces. We studied the Libyan team. We changed our strategy compared to the first match. We are already thinking about the next match against Equatorial Guinea. Our goal is to win the remaining match to stay here in Tangiers.