The Super Eagles – under the guidance of Gernot Rohr – rise to second in Group E with six points from three matches.
They are a point behind leaders South Africa who destroyed Seychelles 6-0.
Nigeria have a chance to enhance or consolidate their two point lead over Libya when the teams meet on 16 October in Sfax in Tunisia.
On Saturday night at the Ahmadu Bello Stadium, Nigeria scored the opener in the fourth minute when Ighalo converted a penalty after he was fouled by the Libya goalkeeper Muhammad Nashnoush.
Ighalo doubled the advantage 13 minutes after the pause and he completed his hat trick mid way through the second half when he slotted in a cross from skipper Ahmed Musa.
Bordeaux winger Samuel Kalu added the gloss in the dying seconds.
“The result does not mean we had a perfect game,” Rohr said after the match. “We had problems defensively especially in the first half. Before we play Libya again we must improve our weak areas.”
The top two from the group will advance to the tournament in Cameroon next summer.