Nigeria and Rwanda both secured narrow wins on Friday at the 2018 African Nations Championship, which leaves the two nations top of Group C with four points each.
The first 45 minutes at Grand Stage de Tanger was a drab affair.
Nigeria's last group game is against Equatorial Guinea next Tuesday in Agadir while Libya will be battling with Rwanda also on the same day.
Faleye, who was looking lively for the Super Eagles, cut inside from the left hand side and unleashed a long range effort which missed the target without troubling Nashnoush in the Libya goal in the 77th minute.
Rayon Sports center defender Thierry Manzi converted a wonderful corner taken by Djihad Bizimana in the 66th minute to put Amavubi in the lead.
Libya has 3 points after thrashing Equatorial Guinea 3-0 in the opening game while Rwanda shared spoils with Nigeria.
Two minutes later, the Shooting Stars forward beat his marker to set up Emeka Ogbugh whose header was saved.
Osas Okoro then played a unsafe curling cross into the Libya box in the 21st minute and Masaud Sand made a crucial clearance as Nigeria continued to press the Mediterranean Knights.
If there is one thing the Super Eagles must get right today, it is their finishing as they registered over 24 shots in the Rwanda game but ended with not even a single goal, albeit they hit the upright thrice.