Marcos Alonso struck the post and a slew of saves from Everton goalkeeper Jordan Pickford also frustrated Chelsea, which came into the game with the second-most goals in the league under attack-minded coach Mauricio Sarri.
Chelsea dropped to third place and two points behind Liverpool after 12 games, but remained unbeaten.
Colombia centre back Yerry Mina made his debut for Everton and was part of a strong defensive effort by the visitors, who look a tougher proposition now that their new coach, Marco Silva, has had three months working on the team's shape and style.
Everton's only loss in in its last seven games has come at Manchester United.
So how did the player perform? Click on the gallery above to find out.
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