Louis Saha struck a superb double to sink Premier League leaders Chelsea at Goodison Park last night.
The Frenchman, celebrating a new two-year contract, took his overall tally for the season to 15 as he cancelled out a Florent Malouda opener and then caught out John Terry for a brilliant winner.
Manchester United's draw at Aston Villa at least meant Chelsea held on to top spot but there were obvious concerns for the Londoners, particularly over the manner of the equaliser.
Saha, who also missed a penalty in an eventful game, powered a fierce header past Petr Cech from a Landon Donovan corner.
The goal meant that of the 22 now conceded by Chelsea in the league this season, 16 have come from set-pieces.
Assistant manager Ray Wilkins said: "When we concede goals we analyse it and we would be disappointed, but these things happen unfortunately.
"We work hard at them but just get a slight lack of concentration.
"It was a good delivery and a good header and we found ourselves losing another goal. From that aspect we are disappointed."
Yet Wilkins conceded that Everton deserved their victory.
He added: "Normally when we go in front we are quite good at keeping hold of it but when you come to a place like Everton, their workrate is such that they make it extremely difficult for you.
"They never lay down and they came back at us in a strong fashion. Looking back over the whole piece, they just about deserved to nick it.
"But full credit to our lads as well, towards the end we came back and had a really good go at them."
Saha was a constant threat to Chelsea and his performance was the perfect response to a challenge from manager David Moyes to score even more goals.
But David Moyes did not go overboard in his praise for the Frenchman.
Moyes said: "He should have got four, not two, so I have challenged him again. I gave him a slight pat on the back but not a full one."
Moyes, however, was at least impressed with the way his top goalscorer troubled Terry throughout the match.
"Louis played really well against him at Stamford Bridge and tonight I thought he did it again," said Moyes, whose side were without Marouane Fellaini and Steven Pienaar.
"I think John Terry was worried when the long ball dropped over the top and Louis took it on his chest.
"But John Terry is a top centre-half and if they don't want him I'll have him!
"It's a terrific result and it just says the way we have been playing in the recent weeks and months.
"To go a goal behind and come back, I don't know how many teams do that against Chelsea.
"We had to hang in because for 20 minutes Chelsea were fantastic."
Chelsea will assess Ashley Cole today after the left-back left the action with an ankle injury in the second half.