Albion defended resolutely throughout, restricting the hosts to few goal-scoring chances.
The Seagulls occasionally posed a threat, themselves, on the counter attack, with the offside flag denying Andi Zeqiri his first goal for the club.
After Cengiz Under also saw his goal ruled out for offside, it looked like the tie was heading for extra-time.
However, Brighton were dealt a cruel blow with just seconds remaining, when Iheanacho turned in Youri Tielemans' cross.
Scroll down and click through to see how journalism student Sam Cox rated Graham Potter's men out of ten.
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5. Ben White - 7
Another assured performance from the ever-impressive Ben White. The 23-year-old nullified much of the Foxes threat and looked comfortable on the ball when trying to turn defence into attack.
6. Steve Alzate - 6
Potter handed Alzate a spot in the starting XI after impressing in the last round against Blackpool and netting the winner at Anfield against Liverpool. The 22-year-old provided energy in both attack and defence but was replaced by Mac Allister in the 78th minute.
7. Jakub Moder - 6
Struggled to make an impression on the game, especially during the second half. Was unfortunate not to register an assist after laying off a fantastically weighted pass to Zeqiri in the 31st minute, but the forward couldn’t make the space count.
8. Adam Lallana - 7
England international Adam Lallana once again provided quality and calmness within the final third. Lallana also performed his defensive duties well when required but failed to impose himself on the cup tie as much as he would have liked.