Thomas Tuchel’s side dominated the encounter but created few chances until Kai Havertz’s shot took a fortunate deflection off Ben Godfrey and beat Jordan Pickford at the near post.
Marcos Alonso, starting ahead of Ben Chilwell in a marauding role at wing-back, twice came close to doubling the lead before Havertz had a goal disallowed for handball.
Jorginho then ensured Chelsea of the three points in the second half, scoring from the spot after Pickford ruined what had otherwise been an excellent performance by bringing down Havertz.
The victory reinforces Chelsea’s position in the top four, with four points now separating them from the Toffees, although both Tottenham and West Ham remain in close pursuit. Here are our player ratings:
Mendy - 6: Was rarely forced into action but played calmly out of the back and dealt with any danger accordingly.
James - 7: Barrelled forward dangerously down the right-wing while limiting any threat from Everton.
Christensen - 7: Another impressive performance from the Dane, who is playing some of the best football of his Chelsea career.
Zouma - 7: Was also a calm presence in defence, rarely - if ever - caught out, and managed to shake off what appeared to be a worrying knee injury.
Azpilicueta - 7: The leader at the back, orchestrating those around him impressively.
Alonso - 8: Many scoffed at the Spaniard usurping Chilwell, but he was fantastic again at wing-back. His runs forward were always dangerous, breaking Everton’s line from deep, and was unlucky not to leave with a goal.
Jorginho - 8: The conductor at the base of midfield, setting the tempo, and scored the decisive penalty.
Kovacic - 7: Commanded possession, touching the ball more than any other player on the pitch, and sets a brilliant axis with Jorginho when they are both on form.
Havertz - 8: One of the German’s best games in a Chelsea shirt, instrumental in both goals and always making dangerous runs in behind. A game that will do wonders for his confidence.
Hudson-Odoi - 7: Made several great runs to drag defenders out of position and was unlucky not to score.
Timo Werner - 5: Still lacks the cutting edge in front of goal and missed two gilt-edged chances late on to get on the scoresheet.
Pickford - 5: Made a number of brilliant reflex saves but ultimately cost his side in taking down Havertz for the penalty.
Digne - 6: Offered a brief threat going forwards but was penned back as Chelsea dominated.
Godfrey - 6: Was bitterly unlucky to concede an own goal having made an impressive start to the game.
Keane - 5: Struggled to deal with the movement of Havertz and Werner, who frequently broke through the line.
Holgate - 5: Was dealt a cruel hand with Alonso’s runs and struggled at times as Chelsea surged forwards.
Iwobi - 5: Had little impact on the game at all and was withdrawn early by Ancelotti.
Allan - 6: Swept up as well as possible in midfield but was overrun as Chelsea dominated possession.
Gomes - 5: Had one shot that stung the palms of Mendy in the first half but failed to seize control of the tempo at the heart of midfield.
Sigurdsson - 5: Did little to cause Chelsea concern with his role as a No 10 rendered all but ineffectual with Chelsea on top for large portions of the match.
Richarlison - 5: Made several dangerous runs but failed to take opportunities when chances presented themselves.
Calvert-Lewin - 5: An unusually quiet game for the striker who was crowded out by Chelsea’s centre-backs.