How the match unfolded
At the other end, Jack Harrison flashed a brilliant volley on the turn just wide of a post.
Chelsea were dealt a blow just before the half-hour mark when captain Reece James was forced off with what appeared to be a repeat of the hamstring injury that kept him out for two months earlier this season.
The hosts took the lead on 54 minutes from a fine counter-attack. After Armando Broja lost possession, Dwight McNeil surged forward and played in Dominic Calvert-Lewin, but after his shot was kept out by Robert Sanchez, Doucoure reacted quickest to strike into the corner of the net.
It means Chelsea have now failed to keep a clean sheet in each of their last nine Premier League matches.
Chelsea pressed for an equaliser, but were unable to convert their 72 per cent possession into goals, with the Everton defence, and Vitalii Mykolenko in particular, standing firm to several attacks from the visitors.
Substitute Dobbin sealed the win two minutes into second-half stoppage time with a shot that went beneath Petrovic from the edge of the area.
A fifth home win in six matches against Chelsea moves 17th-placed Everton on to 13 points.
Chelsea drop to 12th on 19 points following a second successive defeat.
Next five Premier League fixtures
- Everton won with just 28.3 per cent possession, their seventh Premier League win with less than 50 per cent possession in 2023/24, more than any other team this season.
- Lewis Dobbin scored his first goal for Everton aged 20 years and 341 days old, becoming the youngest Toffees goalscorer in the Premier League since Anthony Gordon vs Brighton in January 2022 (20 years and 312 days).
- Sean Dyche put an end to a 10-match Premier League winless streak against Chelsea today, recording his first win against the Blues since August 2017.
- This was the 23rd time that Chelsea have conceded the opening goal in the Premier League in 2023, their joint-most in a calendar year in the competition (also 23 in 1993).