Gylfi Sigurdsson scored the winner from the penalty spot after Edouard Mendy had fouled Dominic Calvert-Lewin, with the Goodison Park faithful treated to a memorable win over Frank Lampard's men upon their return to the stadium.
While Tottenham and Hotspur and Liverpool both managed to accrue just one point from their Sunday fixtures, Leicester's comfortable win over Brighton & Hove Albion means that Chelsea sit outside of the top four heading into gameweek 13.
Here, Sports Mole looks at how the Blues could line up for their clash with Wolves on Tuesday.
Callum Hudson-Odoi, Hakim Ziyech and Christian Pulisic all missed out against Everton with hamstring problems, and while the latter is in the squad for the trip to Molineux, he is unlikely to be risked from the first whistle.
As a result, the front three is likely to remain the same, with Olivier Giroud set to keep his place in the team over Tammy Abraham despite not being able to continue his goalscoring form against the Toffees.
Lampard has options for change in midfield, though, and could be tempted to bring Jorginho into the fold for Mateo Kovacic given the quick turnaround in fixtures. Billy Gilmour is also available, but the teenager is not likely to start this crucial game.
Lampard refused to lay the blame on Mendy for the defeat at Goodison Park after the goalkeeper's rash challenge on Calvert-Lewin allowed Sigurdsson to convert from 12 yards, and Mendy is under no pressure from Kepa Arrizabalaga or Willy Caballero for the number one spot.
Fikayo Tomori will have fond memories of Molineux following his screamer in last season's 5-2 victory, but the 22-year-old has since been frozen out at Chelsea, with Kurt Zouma and Thiago Silva expected to feature from the off again.
Reece James came closest for Chelsea at Everton as his thunderous first-half effort struck the post, and while the Englishman should keep his place in the team, the experienced Cesar Azpilicueta is waiting in the wings and ready to be called upon.
Watch the Sports Mole Football Shorts prediction for this game below: