Late goals from substitute pair Carney Chukwuemeka and Noni Madueke ensured Chelsea reached the semi-finals of the FA Cup after Leicester levelled the game from a 2-0 deficit.
Mauricio Pochettino’s side led 2-0 before the visitors stormed back to level, but a glorious flick from the excellent Cole Palmer set up Chukwuemeka to slot the ball into the corner to put Chelsea 3-2 up before Madueke gave the score some gloss with a brilliant solo effort.
Chelsea were two up at the break thanks to goals from Marc Cucurella and Palmer, while Raheem Sterling had a first-half penalty saved.
A surreal own-goal from Axel Disasi and a Stephy Mavididi goal improbably hauled Leicester back, before Callum Doyle was red carded late on.
Extra-time beckoned, until Pochettino’s subs won it.
Chelsea took the lead after 12 minutes and the move started with a powerful tackle from Moises Caicedo to win the ball on the edge of his own box. One pass released Palmer down the right, and he looked up to see Nicolas Jackson galloping clear and he crossed for the unmarked Cucurella to tap home.
After a strong Leicester opening the goal settled nerves around Stamford Bridge, but this has become a ground used to existing in a state of apprehension.
Robert Sanchez dithered and was nearly dispossessed by Patson Daka, with only good fortune sparing the goalkeeper’s embarrassment. Abdul Fatawu might have done better when he glanced a header wide at the back post from Daka’s cross.
Whatever frustration the winger felt, he moments later allowed it to get the better of him when he crashed through the back of Sterling inside the box for a penalty.
Sterling had scored only six goals in the league this season and took the ball out of the hands of usual taker Palmer, a move he would quickly regret. The penalty was hit low and centrally, and was saved by Jakub Stolarczyk.
He had the chance to make amends for his penalty blunder when sent clear by a fine through-ball from Caicedo but he placed a shot wide with only Stolarczyk to beat.
Sterling finally put things right in the final minutes of the first half. Receiving the ball in the box he ran it almost to the byline and crossed low from the left for the arriving Palmer to make it 2-0.
Chelsea were in full control, but five minutes after the break things altered in ludicrous circumstances.
Disasi received the ball back from a throw-in in the right-back position and was quickly put under pressure by Daka. Turning to play it to his goalkeeper, the Leicester forward nudged him at the moment of contact, and his pass span up and out of his control, sailing over Sanchez for a comical own-goal.
And the tie was level after 62 minutes.
Mavididi cushioned the ball wide on the left, turned and ran at Gusto. The defender backed off and with a swing of the right boot Mavididi sent a fine, arching shot round the dive of Sanchez and in.
It capped a stunning recovery from the visitors, but within minutes they were down to 10 men.
Jackson was tripped by defender Doyle and Andrew Madley initially gave a penalty and showed a yellow card. VAR showed the contact was outside the box, but as the furthest Leicester player back, Doyle saw red.
Madueke came off the bench and saw a first-time shot saved low to his right by Stolarczyk, before he skied one into the Matthew Harding Stand from 12 yards.
The last hope of avoiding extra-time looked to have slipped away. Then came Palmer’s flick, Chukwuemeka’s finish and Madueke’s crowning touch to send Chelsea to Wembley.
