Ross Barkley's second-half goal was enough to send Chelsea into the FA Cup semi-finals, beating Leicester 1-0 at the King Power Stadium.
The result will come as a relief for Frank Lampard after a sloppy first half in which Leicester took advantage of Chelsea's errors but could not find the back of the net, although Christian Pulisic had the best chance of the opening period but was thwarted by an acrobatic Kasper Schmeichel save.
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The Chelsea head coach made three half-time changes and they paid off, with the visitors looking sharper in the second half and one of those substitutes, Barkley, slotted home in the 63rd minute to send the Blues into the Wembley semi-finals.
Later on Sunday, Chelsea were drawn against Manchester United for the next round, which will be played on July 18 and 19. The final will be on August 1.
How Chelsea won again
Leicester began strongly and could have gone ahead inside three minutes. Within 30 seconds, Harvey Barnes had stolen possession before driving towards the area, but he was unable to make the most of a neat interchange with Jamie Vardy.
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Wilfred Ndidi took advantage of some more poor Chelsea midfield play, nipping in before laying the ball off to Barnes on the left. However, his cross - intended for Vardy - was pushed away by the outstretched hand of Willy Caballero.
Leicester: Schmeichel (7), Justin (6), Evans (7), Soyuncu (7), Chilwell (6), Ndidi (7), Praet (6), Tielemans (7), Perez (6), Barnes (7), Vardy (6).
Subs used: Albrighton (6), Choudhury (6), Gray (5).
Chelsea: Caballero (6), James (6), Rudiger (7), Zouma (7), Emerson (6), Kante (6), Gilmour (6), Willian (7), Mount (7), Pulisic (8), Abraham (7).
Subs used: Barkley (8), Kovacic (8), Azpilicueta (7), Loftus-Cheek (6), Pedro (6).
Man of the match: Ross Barkley.
Leicester went close again inside a few minutes as Ndidi again stole the ball back in midfield - this time from N'Golo Kante - to spark a counter-attack, but Dennis Praet's cross evaded Perez, Barnes and Vardy inside the area. Caballero was in action again shortly after to deny Youri Tielemans with a low stop.
Just before the half-an-hour mark, Jonny Evans should have scored with his head. Ben Chilwell - a reported summer transfer target for Chelsea - floated a wonderful free-kick into the area, but Evans could only direct his header wide of the post.
- Leicester made four changes with Nampalys Mendy, Demarai Gray, Kelechi Iheanacho and James Maddison dropping out. Dennis Praet, Youri Tielemans, Ayoze Perez and Harvey Barnes came into the XI.
- Chelsea rung the changes with only five players keeping their places. Antonio Rudiger, N’Golo Kante, Mason Mount, Willian and Christian Pulisic remained in the XI, with the likes of Reece James and Billy Gilmour coming in.
But the best chance of the half came in a rare sight of goal for Chelsea. A sensational pass from Mason Mount found Pulisic in the area, slipping the ball through a tight pocket of space. The USA international then took a few strides before powering the ball goalwards, forcing an incredible fingertip save from Schmeichel.
Lampard's feeling about a slack first half from Chelsea was clear when he made three half-time substitutions, bringing on Barkley, Mateo Kovacic and Cesar Azpilicueta. The visitors were much improved in the second period and Tammy Abraham the ball in the back of the net after 10 minutes - but it was flagged for offside.
Chelsea kept pushing, though, and got their reward in the 63rd minute. After popping the ball between himself and Azpilicueta on the right, Willian floated a cross into the area with Barkley making a run in between Ndidi and Evans to tap the ball home from just outside the six-yard box.
Both sides had the chance for another goal as the game entered the final five minutes. Leicester almost grabbed a late equaliser to send the game into extra time, but Caglar Soyuncu could not direct his header on target. Barkley nearly scored his and Chelsea's second not long after but his strike hammered into the body of Schmeichel before looping behind for a corner.
Chelsea have now reached their 24th FA Cup semi-final and have won their last five games in all competitions, while Leicester's wait for their first ever title win in the competition goes on.
Man of the match - Ross Barkley
What a difference all three substitutes made when they came on at half-time, but none more so than Barkley. He kept making runs inside the area and after a couple of goes at it, it paid off when he slotted home in the 63rd minute in what proved to be the winner.
He continued to be the catalyst up front for Chelsea and almost rounded things off late on, but could only find the body of Schmeichel. Credit must also go to Kovacic and Pulisic - who was by far Chelsea's best player in a poor first half - but for his goal, it's Barkley who takes it.
Lampard said after the game: "I played with Ross and he is a great lad. His attitude has been spot on in training since the minute we've been back.
"He was unfortunate not to start against Villa and since then he has made an impact in every game he has played. He is reaping the benefits. I've got a lot of time for Ross and he is a big player for us."
What the managers said
Leicester manager Brendan Rodgers: "It's disappointing to go out but there are positives. I feel for the players because I think they deserved more than that. The players have maintained that belief in themselves and we just couldn't make the breakthrough.
"It was much more like us and we looked a real threat. That final pass or effort wasn't falling for us. We need to show more conviction, but we have shown all season we can score. It's a performance which will give us more confidence going forward."
Chelsea head coach Frank Lampard: "I don't think we've played that badly this season for 45 minutes. We've played better and lost games.
"I could have made more or different subs. We needed to drag ourselves out of a lethargic performance and we did. We were fortunate to be 0-0 at half-time and we must learn from little mistakes from the game.
"I don't want to sound too down because it's important to show you've got the grit to get a 1-0 win when you don't play well. It looks like I'm criticising but it's positive because it's not the norm for us."
- Leicester have now lost each of their last five quarter-final matches in the FA Cup - with each of the last three all being against Chelsea (also 2012 and 2018).
- Leicester City boss Brendan Rodgers remains winless in all 15 of his meetings with Chelsea as a manager (D8 L7), the most he's faced a single opponent without winning in his managerial career.
- Since his competition debut in January 2014, Willian has been directly involved in 17 FA Cup goals (11 goals, six assists); this is at least six more than any other Chelsea player in this time.
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Leicester are next in action on Wednesday when they travel to Everton, live on Sky Sports (kick-off 6pm). Chelsea will also be playing on July 1 when they take on West Ham in a London derby, also shown live on Sky Sports (kick-off 8.15pm).