With seven changes made to the side that drew 0-0 at Wolverhampton Wanderers on Sunday, young defender Vontae Daley-Campbell made his professional debut for the Football Club, while Jamie Vardy, captain on the night, made his first start since the 2-0 win over Chelsea in January.
In the opening 15 minutes, Cengiz Ünder had a strike blocked in the area, while fellow Turkey international Çağlar Söyüncü hooked clear at the other end as Brighton threatened from a corner, and Vardy then had a shot hit a Seagulls defender.
A brace of wayward efforts from Adam Lallana followed, before a vital interception from James Justin - operating as a left-sided centre-back - prevented the visitors from advancing into a threatening position.
A driven effort from Youri Tielemans came on 36 minutes, but he couldn't test Brighton stopper Christian Walton from distance, and then his hit from a similar distance shortly after could only find the legs of Dan Burn, who got in the way.
The Seagulls were also probing for an opener before the interval, with Andi Zeqiri hooking an acrobatic strike over from inside the six-yard box, as City 'keeper Danny Ward watched the ball sail harmlessly off target.
After the interval, some quick thinking from Walton saw him rush off his line to get in the way of a Justin pass aimed at Ayoze Pérez, however that proved to be the Spaniard's last action of the game after picking up a knock and being replaced by James Maddison, while Ndidi and Vardy made way for Hamza Choudhury and Iheanacho in a triple substitution.
Ünder flashed an effort wide with 64 minutes on the clock, while Zeqiri was denied an opener a minute later when his chipped finish was ruled out for offside in the build-up, and then Ünder also had a goal chalked off for offside, despite firing beyond Walton with a powerful strike.
The lively Zeqiri dragged a shot wide with 18 minutes to play, before Justin had to be taken off on a stretcher after landing awkwardly, with former Austria captain Christian Fuchs replacing the versatile defender on Filbert Way.
Wales international Ward was alert to Switzerland Under-21s forward Zeqiri's low drive on 83 minutes, getting down well before collecting, while Ünder tested Walton at the front post after a beautiful flick from Maddison found the wideman.
In injury time, Tielemans struck the Brighton wall with a free-kick and Burn got himself in the way of Ünder's long-ranger, however City continued to press and in the fourth minute of stoppage time, they found a winning goal.
Substitute Iheanacho was positioned perfectly in the six-yard box to head home a Tielemans cross, following a quick corner, with virtually the last kick of the game to send Leicester into the quarter-finals of the FA Cup.
Major moment
The tie appeared to be heading for extra-time when Vontae Daley-Campbell's run into the penalty area was cut short, and Brighton managed to scramble the ball away for a corner.
However, Nigeria striker Kelechi Iheanacho's movement and headed finish from Youri Tielemans' delivery secured City's spot in the last eight of the competition.
Who impressed?
Speaking on LCFC Radio, Gerry Taggart said: “Well done, Kelechi! To be fair, I'm going to give it to Kelechi. That's exactly what everybody needed!"
Where do we stand?
The Foxes advance to the quarter-finals of the competition, and will find out who they will face in the next round when the draw takes place on Thursday night.
Coming up…
City next welcome Liverpool to King Power Stadium in the Premier League on Saturday (12:30pm kick-off), before they travel to Czech Republic to face Slavia Prague at the Sinobo Arena in the first leg of their UEFA Europa League Round of 32 clash (5:55pm kick-off).
All times GMT.