Substitutes Carney Chukwuemeka and Noni Madueke both scored in stoppage time to send Chelsea into the FA Cup semi-finals.
Chelsea had been two goals to the good at half-time thanks to strikes from Marc Cucurella and Cole Palmer - either side of a Raheem Sterling penalty miss - but the Foxes fought back admirably to level proceedings.
A bizarre own goal from Axel Disasi just after the break pulled the second tier side back into the match, before a wonderful solo goal from Stephy Mavididi levelled proceedings.
Leicester were in the ascendancy after getting back to 2-2, and looked a real threat on the break, but that all changed when Callum Doyle was given his marching orders for a last man tackle, bringing down Nicolas Jackson.
From then on in was one-way traffic as the Blues searched for a winner and the Foxes attempted to drag the game to extra time and penalties, and eventually they got their goal through substitute Chukwuemeka, who slotted home from a lovely Palmer back-heeled pass.
Another late sub, Noni Madueke, scored a long-range deflected goal to wrap the tie up and see Chelsea punch their ticket to another date at Wembley for the semi-finals of the FA Cup.
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