The young Foxes, who are currently sixth in the U18 Premier League South division, headed south to tackle the Seagulls after reaching the quarter-finals of the competition last season.
They were ahead inside just two minutes, too, as Sidnei Tavares was fouled by Ben Clark-Eden in the 18-yard box before stepping up and sending Roco Rees the wrong way from the penalty spot.
However, 15 minutes later, Brighton were back level as the home side were awarded a penalty of their own, with Stefan Vukoje succeeding from 12 yards out to make it 1-1.
Brighton also went ahead with seconds of the first half remaining as Vukoje found the net from the edge of the area with a powerful right-footed finish on the half-turn.
City were awarded another penalty in the 51st minute, though, as goalkeeper Rees felled Tavares, inviting the Portuguese midfielder to convert another spot-kick for the visitors.
The match was settled just after the hour-mark, however, as young Swiss forward Lorent Tolaj applied the finish to a flowing Brighton counter-attack to give the hosts a 3-2 advantage.
Leicester's Under-18s will now return to league duties and are next due to face Aston Villa as the West Midlands club's Bodymoor Heath training ground on Saturday 14 December (11am GMT kick-off).
Goals: Tavares pen 2', pen 51'