The decision came two minutes into added time when Carney Chukwuemeka played a wall with Cole Palmer before slotting in the 3-2 score.
Soon after, Noni Madueke beautifully increased the lead to 4-2.
Before that, Chelsea had made things unnecessarily exciting for themselves after a good start.
Just over twelve minutes had been played when Nicolas Jackson dribbled into the field and found Marc Cucurella with a flat cross. The defender was unmarked at the back post and could easily place the ball in the open goal.
Raheem Sterling then missed a penalty, but made up for it soon after when he served Cole Palmer in front of goal ahead of the 2-0 goal.
Chelsea cruised comfortably into the semi-finals, but Axel Disasi created new excitement after the side switch when he delivered a contender for own goal of the year.
The Frenchman was under pressure when he had to play a pass to his own goalkeeper. The attempted pass was nowhere near finding Robert Sánchez and instead flew into the own goal.
Just after the hour was played, the equalizer also came. Stephy Mavididi dribbled through the Chelsea defense and curled the ball into the far corner to make it 2-2.
Leicester’s Callum Doyle was sent off shortly afterwards and Chelsea took advantage to find the back of the net for a third and fourth time in the game.
(©NTB)