Ross Barkley stepped off the bench to send Chelsea into the last four of the Emirates FA Cup.
The England international was one of three players introduced by Blues boss Frank Lampard at half time following a first period dominated by Leicester.
Leicester City 0-1 Chelsea
2019-20 Emirates FA Cup quarter-final
4pm BST, Sunday 28 June
King Power Stadium, Leicester
And Barkley rewarded his manager by firing home soon afterwards to put the 2018 winners into the semi-finals, and extend the Foxes' 38-year wait to reach the last four of the competitions.
Leicester had named a strong starting XI, although James Maddison was ruled out by an injury. Chelsea, meanwhile, made six changes from their Premier League win over Manchester City on Thursday with Billy Gilmour, who impressed in their fifth-round win over Liverpool, among those drafted in.
Before the game, both sides paused to pay tribute to the National Health Service's work during the COVID-19 pandemic as well as showing their support for the Black Lives Matter movement.
Leicester came flying out of the traps, with Harvey Barnes seizing on some indecision in the Chelsea defence and playing a one-two with Jamie Vardy to get in on goal inside the opening 15 seconds only for the ball to outrun him.
Moments later Barnes was involved once again, with his low cross being palmed away by Caballero as Vardy lurked. Former England striker Vardy also saw a delivery of his own blocked soon afterwards.
Chelsea found their feet but continued to look shaky at the back, with Leicester carving out the first chance of the game when Ben Chilwell's free kick found the head of Jonny Evans only for the Northern Irishman to flick wide of the far post.
That seemed to fire the away side into life, with Christian Pulisic drawing a superb save from Foxes goalkeeper Kasper Schmeichel on the half-hour.
Vardy had a good chance to break the deadlock just before the interval when he latched onto Wilfred Ndidi's pass over the top of Chelsea's defence, but he pulled his shot across goal and wide of the far post.
Chelsea manager Frank Lampard was clearly unimpressed by his side's first-half performance, to the extent that he made a triple substitution at the break.
One of those substitutes, Mateo Kovacic, was instrumental in helping the visitors make a strong start to the second period, while the combination between Pulisic and Tammy Abraham began to test the Foxes' rearguard.
Abraham – without a goal since 11 January – did have the ball in the net ten minutes after the restart, but he was immediately ruled offside without the need for VAR to intervene.
Instead it was another of Lampard's first-half introductions that did open the scoring when Barkley steered Willian's right-wing cross past Schmeichel on 63 minutes.
Chelsea continued to dominate after their goal, although Leicester did threaten through Vardy, who saw a shot well blocked by Kurt Zouma, while Ben Chilwell drew a good save from Caballero.
The Foxes ended the game strongly and almost levelled a few minutes from time when Mark Albrighton's inswinging cross deceived the Chelsea goalkeeper and found the head of Caglar Soyuncu, but his effort deflected off Cesar Azpilicueta and over the unguarded goal.
Barkley almost wrapped things up and added his second, but his driven shot at the end of a rapid counter-attack was turned over the bar by Schmeichel.
And so it is Chelsea whose aim of winning the Emirates FA Cup for the ninth time is still alive with Lampard, who played in four of those successful campaigns, the man leading them to Wembley.
Leicester City: 1 Kasper Schmeichel (C), 2 James Justin, 3 Ben Chilwell, 4 Caglar Soyuncu, 6 Jonny Evans, 8 Youri Tielemans, 9 Jamie Vardy, 15 Harvey Barnes, 17 Ayoze Perez, 25 Wilfred Ndidi, 26 Dennis Praet
Substitutions: 11 Mark Albrighton for Perez 57', 20 Hamza Choudhury for Praet 57', 7 Demarai Gray for Barnes 76'
Unused substitutes: 12 Danny Ward (GK), 5 Wes Morgan, 14 Kelechi Iheanacho, 24 Nampalys Mendy, 28 Christian Fuchs, 29 Ryan Bennett
Yellow card: Soyuncu 23'
Manager: Brendan Rodgers
Chelsea: 13 Wilfredo Caballero, 2 Antonio Rudiger, 7 N'Golo Kante, 9 Tammy Abraham, 10 Willian, 15 Kurt Zouma, 19 Mason Mount, 22 Christian Pulisic, 24 Reece James, 33 Emerson, 47 Billy Gilmour
Substitutions: 8 Ross Barkley for Mount 46', 17 Mateo Kovacic for Gilmour 46', 28 Cesar Azpilicueta for James 46', 12 Ruben Loftus-Cheek for Pulisic 72', 11 Pedro Rodriguez for Willian 78'
Unused substitutes: 1 Kepa Arrizabalaga (GK), 3 Marcos Alonso, 5 Jorginho, 18 Olivier Giroud
Goal: Barkley 63'
Manager: Frank Lampard
Referee: Mike Dean