The Eagles battled hard to break the defence of the Libyans and won the first encounter played at the Godswill Akpabio International Stadium in Uyo, the Akwa Ibom State capital.
It was Lazio of Italy midfielder, Fisayo Dele-Bashiru, who came off the bench to score for the three-time African champions in the game where the Libyans camped in their own half most part of the 90 minutes defending with grit.
Dele-Bashiru, who replaced Alex Iwobi in the 74th minute, scored in the 86th minute after connecting well with a low cross from Moses Simon.
Nigeria currently lead the Group D with seven points after three games, while Benin Republic closely follow with six points, with Rwanda and Libya having two points and one point.
Nigeria will face the Libyans for the return leg on Tuesday at Benina Martyrs Stadium in Libya.
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