Everton inflicted a third consecutive away defeat on Chelsea, who also lost captain Reece James to injury
Having kept the visitors at bay relatively comfortably, 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.
One downside to the afternoon for the hosts was fifth bookings of the season for defender Jarrad Branthwaite and midfielder Idrissa Gueye. The pair will be suspended for the trip to strugglers Burnley.
The loss of the former - excellent again in his partnership with James Tarkowski - will be a particular blow as Dyche is not blessed with centre-back options. Unused substitute Ben Godfrey's only Premier League appearance came in the 89th minute in September while Michael Keane was not even in the matchday squad.
But this Everton team thrives on adversity, as they have shown since the 10-point deduction for breaching financial regulations last month.
Since being plunged into the bottom three following the punishment by an independent commission they have taken nine points from a possible 12.
Their extended run is 13 points from six with just one defeat and without the penalty Everton would be above their opponents in 10th.
The first half was significant only for injuries to both teams' starting right-backs - Reece James and Ashley Young - a Cole Palmer booking for diving and Jordan Pickford saving the only shot on target from Palmer's 20-yard curler.
Gueye was replaced by the fit-again Amadou Onana at half-time and buoyed by the confidence of Thursday's win and the fact the visitors had not really hurt them, Everton set about formulating a response.
Winger Dwight McNeil, who has had a growing influence in recent games, had a low shot tipped around the post by Robert Sanchez before threading a pass through to Dominic Calvert-Lewin.
Although the England international's attempt was charged down by Sanchez, who clattered into the striker in the process and later departed injured, the loose ball rolled to Doucoure and he drilled home his fifth of the season.
Branthwaite's foul and booking gave Chelsea a free-kick 20 yards out but Pickford comfortably held Palmer's low, drilled effort.
Chelsea sent on Raheem Sterling and Nicolas Jackson to boost their attacking options but Pickford continued to be under-employed.
That was in part due to the increasing resilience of the defence in front of him, with bodies being thrown in all directions to keep out the threat.
"You can stick you points deduction up your a***" rang out in the closing stages at Goodison Park, where late substitute Dobbin wrapped up victory in the second minute of stoppage time.
