Egypt was defeated by the Super Eagles in the AFCON opener.
After 30 minutes, Iheanacho scored with a half-volley from the edge of the box into the top corner, but Nigeria should have added at least a couple more goals in what was the best performance by a team in the finals so far and a warning to their rivals.
Egypt could not get out of first gear and could not bring talisman forward Mohamed Salah into the game, as he cut an isolated figure up front, starved of service and the quality needed to have an impact.
Sudan will face Guinea-Bissau in the second game of Group D later on Tuesday at the same venue.
Egypt was shocked by the injury to right-back Akram Tawfik in the first 10 minutes, and he appeared to be in pain as he was helped off the field.
Nigeria found plenty of joy down that flank in his absence, with Moses Simon profiting and causing constant concern for the Egyptians.
As he found space in the box, Simon had his first sight of the goal, but as the angle narrowed, he could only fire into the side-netting.
However, Nigeria quickly took the lead, and the move once again began with him. Iheanacho scored the game-winning goal, giving Egypt goalkeeper Mohamed El Shennawy no chance.
When the ball came close to Salah, he was surrounded by two or three defenders, but Egypt was unable to exploit the space created by Nigeria’s doubling up on their lead forward.
Nigeria hit the crossbar early in the second half when Taiwo Awoniyi’s close-range header was deflected onto the goal frame by El Shennawy before Iheanacho squandered a fantastic chance to double the lead when the ball fell to him in acres of space in the box, but a poor first touch let him down.
Salah finally got a scoring opportunity on 70 minutes, but he couldn’t get any power into his effort due to pressure from two defenders and the keeper.
Nigeria looked the most likely to score, and the pace of their wingers and fullbacks stretched the more pedestrian Egyptians on several occasions.
The result moves Egypt’s hopes of adding to their record-setting seven AFCON titles ahead of Saturday’s clash with Guinea Bissau.
Nigeria, on the other hand, will be full of confidence heading into their next Group D match against Sudan on Saturday.