Willian's stoppage-time effort proved the winner, adding to Antonio Rüdiger's first-half header, with Dominic Calvert-Lewin's 94th-minute effort proving only a consolation as Everton - under the temporary charge of David Unsworth - bowed out of the competition.
Antonio Conte returned to the side that saw his team advance to this stage of the competition, keeping faith with the youngsters that were impressive against Nottingham Forest in the previous round.
The home side dominated the opening half, which saw Danny Drinkwater make his long-awaited debut for the club having been injured since arriving from Leicester City on deadline-day.
In a first-half that did not really consist of a lot of action but the Blues managed to score the opening goal of the night with a short corner from Willian, who found Charley Musonda.
The young Belgian winger crossed the ball deep into the box to find an unmarked Rüdiger, who powered a difficult looping header over Jordan Pickford in goal, scoring his first for Chelsea.
Davide Zappacosta had an opportunity to add a second for Conte's chages in the first-half, however, he saw his effort hit the side-netting after being found by Willian.
Action in the second-half picked up
Everton began the second-half in a more attack-minded fashion, with Unsworth's side becoming more physical with their challenges.
Tom Davies was shown a yellow card for a challenge on Ethan Ampadu, whilst James McCarthy also picked up a booking for catching Kenedy.
Willy Caballero was finally called into action by the Toffees when Wayne Rooney had a glorious chance to score, however, the Spanish goalkeeper managed to somehow keep the ball out of the back of the net, without knowing too much about it.
The former Manchester City shot-stopper had been involved moments before, making a good save before a moment of madness nearly cost his side the lead.
Conte decided to freshen his attack up after bringing Cesc Fábregas, Pedro and Álvaro Morata on to see things out. However, the final moments of regular time and stoppage time saw the most exciting moments of the game.
Exciting final moments
Chelsea doubled their lead through a stunning goal by Willian, who played a delightful one-two with Fábregas and smashed an effort past Pickford off the inside of the post, leaving the keeper with absolutely no chance of stopping the ball.
Everton did manage to pull one back, with Calvert-Lewin - who came on as a substitute for McCarthy - netting a goal, but it was too late to spark a real comeback.
Chelsea will now have to wait until Thursday's draw to see who they will face for a place in the final four of the tournament.