Rwanda continued a good run at the ongoing 2018 African Nations Championship (CHAN) after winning 1-0 in the second game of Group C against Equatorial Guinea at Grand Stade de Tanger, Morocco on Friday night.
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.
Rwanda are now joint-top of Group C with the home-based Super Eagles of Nigeria on four points.
In the 79th minute, the Eagles then got the match's winning goal via Faleye.
The only shot on target in the first-half came on the half-hour mark when Libyan Mohamed Aleyat's free-kick was saved by Nigeria goalkeeper Ikechukwu Ezenwa.
Nigeria were finding it hard to penetrate the Libyan defence which was marshalled by Ahmed El Trbi, who put his body on the line in the 40th minute - blocking Stephen Eze's thunderous long-range shot.
Nigeria did most of the attacking in the early stages of the second-half and almost broke the deadlock in the 55th minute.
The first chance of the second half fell to Ogbugh in the 55th minute as he headed a cross from Sunday Falaye straight at Libya keeper Muhammad Nashnoush.
Constant fouling meant the match never developed a rhythm and neither side created a clearcut scoring opportunity until Faleye netted 11 minutes from time.
Rwanda and Nigeria are leading the table with four points after drawing one game and winning one while Libya dropped to third position after losing to Nigeria 1-0.