The former Manchester City striker scored three goals on the night, one counted easily, the other two were disallowed but one eventually overturned.
Iheanacho scored in each half but it was his strike 13 minutes from time that required the intervention of the video assistant referee.
"I didn't know if I was onside or offside but I agree totally now that I was onside", Iheanacho told BT Sport.
VAR's first ever goal was awarded to Leicester, while fellow Premier League side West Ham were made to wait until extra time before managing to overcome Shrewsbury.
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He has now scored three goals in all competitions this season since his big-money move from Manchester City.
However, a review of the goal via VAR clearly showed Iheanacho was onside when Mahrez played him in - ensuring Leicester were 2-0 up and on the way into round four, while their 21-year-old forward will be the answer to a trivia question for years to come.
The striker was slipped in by Mahrez and finished calmly, and although it was originally given as offside, the goal was eventually given after referee Jon Moss consulted with the VAR.
The England worldwide missed an emotional return to the club he helped gain promotion to the Football League in the original third-round tie, 10 days ago.
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League One side Fleetwood will be attempting to beat opposition from a higher division in an FA Cup away game for only the second time in their history.
It's still a fairly embarrassing result for West Ham, but nonetheless they are safely through to the fourth round where they will face either Bournemouth or Wigan Athletic, who replay on Wednesday.
Meanwhile, Cardiff will host Manchester City next after they saw off Mansfield Town.
It was a surprise when Leicester went ahead two minutes before half-time and the goal came from nothing.
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Wednesday will now play Reading in the fourth round after they beat League Two Stevenage at the Madejski Stadium, thanks to Jon Dadi Bodvarsson's hat-trick.