Steven Naismith, who was introduced as an early substitute, did all the damage for the home side with a brilliant hat-trick. Not even a Nemanja Matic wonder strike could rouse Chelsea from the doldrums.
Seeking to fix a suddenly leaky defence, Mourinho made two key changes. He dropped floundering centre-back Gary Cahill in favour of the younger, quicker Frenchman Kurt Zouma.
The move meant Chelsea had extra pace at the back to deal with Everton forwards Arouna Kone and ex-Stamford Bridge man Romelu Lukaku. But Mourinho also swapped Brazilian forward Willian for midfield destroyer John Obi Mikel. The move was clearly designed to offer more protection in front of the men at the back.
The only other notable change involved Asmir Begovic stepping in for injured goalkeeper Thibaut Courtois.
Chelsea's official Twitter feed provided the full starting 11:
Meanwhile, the Liverpool Echo detailed Everton's lineup:
The midfield balance Toffees boss Roberto Martinez sought to create was disrupted early on when the talented Muhamed Besic succumbed to an apparent hamstring injury. Everton had to turn to forward Naismith in the Bosnian's place. They would soon be glad they did.
That initial setback didn't stop the Goodison Park faithful making light of Chelsea's failed summer pursuit of Stones, per Echo reporter Phil Kirkbride:
Despite the banter, it was Chelsea on the front foot for most of the early stages. In particular, Pedro proved a danger from the flanks. The former Barcelona man gave young left-back Brendan Galloway a tough time.
But it was Naismith who made the game's first decisive contribution. The Scot linked well with Galloway, who had started to make some dangerous runs forward.
The full-back returned the ball with a fiercely whipped cross that Naismith rose to turn into the net with a deft header. Kirkbride noted how scoring against Chelsea is something of a trend for the ex-Rangers star:
Everton kept the pressure on and it took a fantastic fingertip save from stand-in Begovic to deny Kone a certain goal. Begovic was forced to deny James McCarthy soon after as Everton pushed for another.
But the former Stoke City stopper could do nothing when Naismith rasped a low drive into the bottom corner seconds later. WhoScored.com detailed how the goal emphasised Chelsea's problems at the back:
Everton were breaking too easily through the Chelsea midfield, a trio that consistently left the struggling defence exposed, despite Mourinho's changes.
There was a slight fightback from Chelsea as Tim Howard saved to deny raiding full-back Cesar Azpilicueta. But Chelsea continued to struggle keeping pace whenever the hosts counter-attacked.
Lukaku soon turned markers inside out and whipped a ball across the box that was hastily cleared for another Everton corner. There was just too much space in the middle and no pressure on the man in possession from the visitors.
The first half was going stale until Matic hit a terrific left-footed drive to get Chelsea back in it. He curled his long-range shot over Howard with stunning power and technique.
Eden Hazard then saw a shot deflect just wide for a corner. Terry headed over from the ensuing set piece and then Ivanovic inadvertently deflected Hazard's long-ranger away from Howard.
Mourinho wisely began the second half by subbing Mikel for Brazilian Kenedy. It was a necessary attack-minded change. Chelsea's Twitter feed explained how Mourinho's men changed shape:
But it was Lukaku who pressed for the half's first chance. Terry got lucky after a pretty obvious back pass helped Begovic gather with Lukaku closing in. The young Belgian striker was causing problems every time he roamed wide.
Kone and Ross Barkley wasted good opportunities for Everton, before Howard had to palm an Azpilicueta cross wide. Pedro was still causing problems but tried to buy a penalty with an unconvincing dive.
Both managers made changes, with Martinez introducing Aaron Lennon for Kone, while Mourinho brought on striker Radamel Falcao for Pedro. As a final roll of the dice, Mourinho also swapped Fabregas for Willian.
Martinez was forced into another reshuffle when right-back Seamus Coleman had to go off. The answer was to put Stones in his place and introduce new signing Ramiro Funes Mori in the middle.
A subdued second half, unusually so given the score at the break, was lit up by Naismith's hat-trick goal inside the final 10 minutes. Some superb combination passing involving Barkley freed Naismith from close range and the Scot swept it in from a tight angle.
Simon Johnson of the London Evening Standard offered a damning verdict on what the goal means for Chelsea's already ailing title defence:
For Naismith, it wrapped up a perfect hat-trick, according to Squawka:
After the game, BT Sport analyst Paul Scholes declared Mourinho is facing "one hell of a job" to repair Chelsea's season, per BT Sport Football Twitter:
As for Martinez, he expressed his pride and satisfaction with Everton's team performance, during an interview with BT Sport's Jake Humphrey:
Martinez also praised hat-trick hero Naismith. The player himself used his post-match interview to reveal how he resisted interest to leave Goodison Park during this summer's transfer window:
Even after yet another dismal performance, Mourinho preferred to believe fate is conspiring against his side:
Not for the first time this season, Mourinho felt his team deserved more:
The defending champions are now in such dire straits, Johnson even believes their first UEFA Champions League opponents will be a problem:
Chelsea will now head into the start of their Champions League campaign on the back of a nightmare start domestically. Three defeats and just one win out of five leaves Mourinho on the brink.
For Everton, the win is a reminder of the quality Martinez has in his ranks. It's now time for the Spaniard to put together a legitimate push to finish in the European places.