Everton inflicted a third consecutive away defeat on Chelsea, who also lost captain Reece James to injury.
Abdoulaye Doucoure struck early in the second half and substitute Lewis Dobbin drilled home his first Premier League goal in added time as Everton moved four points clear of the bottom three despite their points deduction.
Chelsea had 71 per cent possession but familiar failings up front cost them and Mauricio Pochettino’s side have now won just twice in eight league games.
The loss of James was a blow for Chelsea, while Everton will be without Jarrad Branthwaite and Idrissa Gueye for their next game due to suspension.
Everton have taken nine points from a possible 12 since being plunged into the bottom three following the punishment by an independent commission for breaching financial regulations last month.
The first half was quiet, with both teams losing their starting right-backs to injury. The only moment of note came when Jordan Pickford saved Cole Palmer’s shot.
Gueye was replaced by Amadou Onana at half-time and Everton started the second half brightly. Dwight McNeil had a shot tipped around the post by Robert Sanchez before threading a pass through to Dominic Calvert-Lewin.
Calvert-Lewin’s attempt was charged down by Sanchez, but the loose ball fell to Doucoure and he drilled home his fifth of the season.
Chelsea sent on Raheem Sterling and Nicolas Jackson to boost their attacking options but Pickford continued to be under-employed.
Everton’s defence was resilient and they were able to hold on for the victory. Dobbin wrapped up the win in the second minute of stoppage time.
The result means that Everton move four points clear of the bottom three, while Chelsea have now won just twice in their last eight league games.