Gernot Rohr's side registered their second group win of the 2019 AFCON qualifiers against Libya.
The Super Eagles started the game on the front foot and were awarded a penalty as early as the third minute when Odion Ighalo was brought down and he stepped up to convert the resulting penalty.
The game became a tussle with both sides trying to assert themselves as the Libyans occasions causing the Super Eagles a scare.
Alex Iwobi struggled to boss the game for the Super Eagles along with companions Wilfred Ndidi and Oghenekaro Etebo with defender Jamilu Collins going the closest when his solo run hit the cross bar.
The game ended 1-0 in favour of the Super Eagles at the halftime break courtesy an Ighalo penalty.
The Super Eagles started the second half with more intensity with Ahmed Musa asking questions of the Libyan goalkeeper.
Persistent pressure paid off as Ighalo doubled the Super Eagles lead when he latched onto a well weighted ball to him by Arsenal midfielder Iwobi.
Ighalo scored his third of the game when he got on the end of a cross by Musa to rebound his shot into the net .
He was substituted for Watford forward Isaac Success to a standing ovation to the supporters from the Godswill Akpabio Stadium.
Samuel Kalu scores fourth goal of the game when he curled a shot past the goalkeeper after he received a pass from Henry Onyekuru.
The result means that the Super Eagles picked up their second group stage win in the group and now have six points with South Africa top with seven points after a 6-0 win over Seychelles.
The Super Eagles return to action when they travel to Tunisia to face Libya in the second leg on Tuesday, October 16.