In a game that severely lacked quality, the former Manchester City forward leapt highest just seconds before the final whistle to secure the Foxes victory.
Story of the Match
Seagulls enjoy promising opening half
There was not all too much to write home about during a first-half that flattered to deceive. The visitors just about edged the opening period though with Adam Lallana twice firing over and Andi Zeqiri sending an acrobatic effort off target.
Leicester almost livened the game up immediately after the break and in bizarre circumstances. A deep free-kick from Cengiz Under bounced off of Dan Burn and looked to be heading into the Brighton goal but fortunately for the Seagulls it bounced wide.
Offside flag denies openers
Even when it looked like the scoring had been opened as Zeqiri netted with a great, lofted finish after being played through, the celebrations were cut short by the offside flag.
The Foxes were also denied by the flag as they then thought they had struck first. Substitute Iheanacho was played through, then falling as he attempted to collect. Somehow, he managed to nudge the ball inside, with it then falling for Under to lash home but his joy was short-lived, too.
Worrying injury news for Leicester but Iheanacho steps up
Coming into the game, the last thing that Leicester needed were more injuries and that is exactly what happened. Going down unchallenged, James Justin appeared to jar his knee and had to be carried off the pitch on a stretcher.
It wasn't quite all bad news though as Leicester booked their quarter-final ticket late on. A short corner caught the Seagulls out, with everybody failing to spot Iheanacho at the far post. He then ghosted in undetected to get on the end of Youri Tielemans' cross and head beyond Christian Walton.
Fingers crossed for Justin
One of the players of the season so far for the Foxes, it was certainly worrying to see James Justin go down through injury. Hopefully, the problem doesn't look as serious as first feared as he has been excellent for Leicester all campaign long.
Prior to the meeting with Brighton, he had played every single minute of the Premier League campaign, turning in impressive defensive performances whilst also netting two goals. He will definitely be a miss if he is ruled out for an extended period of time.
Lack of quality
Despite the late drama, the game will not be remembered for a long time in the minds of supporters. There really was a severe lack of any goalmouth action.
There were no shots on target at all until the final ten minutes, with the only goal coming in practically the last moment. Whether that is down to a host of changes from both managers remains to be seen but Brendan Rodgers and Graham Potter will surely be hoping for more in the next match.
One real positive for both teams will be the performances of their debutants. Rodgers called up youngster Vontae Daley-Campbell for his first ever Foxes' appearance and he performed extremely well at right-back, even playing a key role in winning the corner that led to Leicester's winner.
Meanwhile, Polish duo Jakub Moder and Michal Karbownik made their first appearances for the Seagulls and looked extremely capable and will surely be afforded more opportunities going forwards.