The Super Eagles who are three-times AFCON champions had an upper hand in the game with a ball possession of 56% as compared to 44% of the Pharaohs.
Pressure mounted on Liverpool star and Egypt's Captain Mohammed Salah when Leicester City striker Kelechi Iheanacho gave Nigeria the lead in the 30th minute.
The Pharaohs searched for an equaliser but the solid Super Eagles' defence cleared all their goal-scoring opportunities.
The Super Eagles almost stretched their lead to 3-0 when they came blazing in the 48th and 65th minute but hit the crossbar.
Moh Salah beat Nigeria's offside trap in the 71st minute but his shot was cleared in the box.
Two minutes in extra time, the Super Eagles' Chidera Ejuke almost found the back of the net after rounding up several Egyptian players but hit the side net. Full-time, Nigeria 1 Egypt 0.
In the last AFCON encounter on Tuesday, Guinea-Bissau and Sudan drew 0-0. Guinea-Bissau's Midfielder Pele saw his 82nd-minute spot-kick kept out by Sudan goalkeeper Ali Abou Achrine and Piquet hit the crossbar from the rebound.
Today's AFCON fixtures:
Group F: Tunisia vs Mali, 3 pm (Limbe Stadium, Limbe).
Group F: Mauritania vs Gambia, 6 pm (Limbe Stadium, Limbe)
Group E: Equatorial Guinea vs Ivory Coast, 9 pm (Japoma Stadium, Douala).