Nemanja Matic’s spectacular strike from distance dragged Chelsea back in the game at Goodison Park after early substitute Steven Naismith had scored twice.
Naismith, who has scored more goals against Chelsea than any other Premier League side, came on after eight minutes when Muhamed Besic limped off with a foot injury.
And on 16 minutes, the Scotland forward maintained his fine record against the Blues when he slipped the ball to Brendan Galloway and continued his run to head home the left-back’s cross.
Asmir Begovic, standing in for the injured Chelsea keeper Thibaut Courtois, then denied Arouna Kone and James McCarthy as Everton grew in confidence.
And the home side did not have to wait long for a second goal, as Chelsea allowed Everton to work the ball to Naismith, who drilled in from the edge of the box.
Having been rattled, Jose Mourinho’s side responded well. Cesar Azpilicueta had a shot blocked by John Stones, who impressed in the first half against the club who chased his signature all summer.
It took a bolt from the blue though to reduce the arrears as Matic, a good 35 yards out, launched a swerving shot which beat Tim Howard in the home goal.
And Chelsea could have been level shortly afterwards, but John Terry – returning to the side after suspension – headed over from an Eden Hazard cross.
Subs: Robles, Mirallas, Lennon, Naismith, Deulofeu, Osman, Funes Mori.
Chelsea: Begovic; Ivanovic, Zouma, Terry, Azpilicueta; Mikel, Matic; Pedro, Fabregas, Hazard; Costa.
Subs: Blackman, Cahill, Loftus-Cheek, Kenedy, Willian, Falcao, Remy.