Richarlison headed them into the lead after Kepa Arrizabalaga parried Dominic Calvert-Lewin’s header into his path.
Gylfi Sigurdsson sealed the win, scoring at the second attempt after Arrizabalaga had saved his penalty.
Chelsea remain three points behind fourth-place Arsenal and a point adrift fifth-place Manchester United.
Eden Hazard went close for the Blues with a curling effort that came off the post and Jordan Pickford made a great save to deny Gonzalo Higuain.
The Toffees move above Bournemouth into 11th with 40 points.
Everton 2 – 0 Chelsea | English Premier League – Match Highlights
- 49′ 1 – 0 Richarlison heads in from close range for Toffees. It’s been coming! Dominic Calvert-Lewin’s header is fired at goal but Kepa makes a good save to keep it out. Richarlison reacts quickest to pounce on the rebound and nods it into the top of the net from just a few yards out.
- 72′ 2 – 0 Gylfi Sigurdsson scores after his penalty is saved! Gylfi Sigurdsson doesn’t hit it well and his penalty is well saved by Kepa, who dives the right way to his right. Unfortunately for the Chelsea keeper, the rebound falls straight in the path of Sigurdsson and he slots it into the corner. Penalty to Everton after Marcos Alonso just clips Richarlison in the box and Anthony Taylor points straight to the spot. Gylfi Sigurdsson will take.