Iheanacho put Leicester 1-0 up in the 44th minute after coolly slotting the ball past Fleetwood keeper Chris Neal following Islam Slimani’s through ball.
And in the 77th minute, Iheanacho made it 2-0 with a delightful lofted finish over Fleetwood keeper.
The goal was initially ruled out for offside but was eventually given after the use of the Video Assistant Referee (VAR).
It was a historic decision because that was the first time ever in English football that a goal would be awarded after a VAR review.
Iheanacho was later replaced by Shinji Okazaki on 81 minutes.
Leicester will now travel away to face another League One club Peterborough FC in the fourth round.
The last time Iheanacho scored for Leicester was in a 3-1 home win against Leeds in the Carabao Cup on October 24, 2017.
He has now scored three goals in all competitions for Leicester since joining them from Manchester City last summer.
And in other third round replays on Tuesday, Cardiff City defeated home side Mansfield Town 4-1, while Sheffield Wednesday beat visiting Carlisle United 2-0.
FA Cup 3rd round replays:
Leicester City 1-0 Fleetwood Town
Mansfield Town 1-4 Cardiff City
Sheffield Wednesday 2-0 Carlisle United