Chelsea and Jose Mourinho were plunged into further trouble with a 3-1 defeat at Goodison Park, a hat-trick from Steven Naismith giving Roberto Martinez’s side victory.
The defeat represents Chelsea’s worst start to a season since 1988, and their bid to retain the Premier League title already looks doomed.
Naismith, a ninth-minute replacement for the injured Muhamed Besic, scored twice within moments of coming on as Everton turned up the heat on Jose Mourinho’s out-of-form side.
Nemanja Matic pulled one back with a fine strike before half-time at Goodison Park but Naismith rewarded the hard-working Toffees by completing his treble after 82 minutes.
It was the first time a Mourinho Chelsea side had conceded a hat-trick and the result left them with just four points from five games.
Further frustration for Mourinho was that John Stones, the England centre-half he tried so hard to buy over the summer, was outstanding in Everton’s back four.
The hosts’ afternoon actually began badly as Besic, making his first Premier League appearance of the season, was hurt in an early challenge by Kurt Zouma.
His misfortune proved a blessing in disguise for Everton, however, as his replacement Naismith ran the Londoners ragged.
There was an early warning for the visitors as Naismith went close to getting on the end of a dangerous Seamus Coleman cross.
That was not heeded as Naismith was allowed to turn after 17 minutes, feed Brendan Galloway on the left and then get in the box to head home a return cross.
It could have got considerably worse for Chelsea but goalkeeper Asmir Begovic, in for the injured Thibaut Courtois, brilliantly saved from an Arouna Kone header and a long-range James McCarthy strike.
But Everton kept attacking and gained further reward when Naismith found the target with a powerful effort from distance.
Chelsea were rocking and there were possible signs of frustration as Coleman caught a stray arm from Diego Costa in the face.
The champions did eventually start to settle and play some neat football up to the Everton box.
They hauled themselves back into the game with a stunning long-range strike from Matic after 36 minutes – his first Premier League goal since scoring in Chelsea’s 6-3 win at the same venue last year.
Eden Hazard then had two chances blocked and John Terry, back from suspension, headed narrowly over as Chelsea finished the first half in the ascendancy.
Chelsea were a more forceful proposition after the break and controlled much more possession.
But Everton’s back four, superbly led by Stones and Phil Jagielka, held firm and gave their side a platform to launch some counter-attacks.
Romelu Lukaku broke away from Branislav Ivanovic but shot at Begovic. Everton appealed for a back-pass as the ball rebounded off the keeper and back into his arms via Terry’s feet but referee Andre Marriner did not see it as deliberate.
Kone also tested Begovic on another counter-attack, but principally their job became defending as Chelsea probed for an equaliser.
But they still struggled to create clear-cut chances and Tim Howard was well protected.
Nasimith applied the killer blow eight minutes from time as he latched on to a through-ball from the excellent Ross Barkley, took the ball wide of Begovic and then fired home from a tight angle.
Stones ended the game at right-back after Coleman went off injured but Everton held out.