With Fernando Torres now officially written off as a flop and packed off to AC Milan and Demba Ba doing similar at Besiktas, Mourinho fortified his attacking lineup in the offseason.
Didier Drogba replaced Samuel Eto'o in the veteran role while imminent arrival Loic Remy's pace will give Chelsea yet more firepower. It would not be remiss to say at this stage, however, that Diego Costa is the difference between Chelsea being a mere title hopeful and Chelsea leading the Premier League race from the front.
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He dominated Everton, quite literally from minute 1 to 90, with a goal at either end to bookend this match. There could have been more from the strapping Spain international, who looked composed and at home as the mischief-maker in Mourinho's team.
The Chelsea manager's natural inclination is usually to shut teams down once his own has gone in front. Doing that here merely played into Everton's hands. Roberto Martinez likes his team to have the ball and be the aggressor.
It was not due to its defensive strength or tireless workrate in midfield that Chelsea won this game so convincingly — it was the fact, that in the second half, the Blues showed they are willing and capable of going on the offensive in an attempt to see the game out.
"At halftime we were winning 2-1," Mourinho said. "I was telling them that against a team like Everton you cannot sit back and defend for 45 minutes. You have to try to hurt them, you have to try to score goals."
This edict was demonstrated most precisely in the performance of Nemanja Matic. Often a pivot in Mourinho's midfield who scarcely crosses midfield, he was aggressive and dominant all along the middle third. He claimed a goal and an assist and led the fight capably.
Cesc Fabregas will be central to any Chelsea assault on the Premier League title and Champions League and here he demonstrated his capabilities right from the outset. He had too much space in midfield and, in the absence of significant pressure, he played an immaculate pass to the run of Costa.
He was the man, too, who should have provoked a red card on Tim Howard. Fabregas' pass for Eden Hazard was again well-judged. The American raced from his goal and handled outside the area. The incident was missed by Jon Moss and his assistant referee and Everton escaped. The game was 10 minutes old at that stage and the hosts were already two down, as good as beaten.
Chelsea maintained that intensity, which served it well from the beginning. A Ramires pass to Branislav Ivanovic caught Leighton Baines playing an attempted offside trap badly and the Serb made no mistake.
At that stage there was a palpable energy about the visitors. Matic broke up the play and gave it to those in yellow more skilled than he is. Willian linked the play together. Fabregas buzzed menacingly.
Just like that, however, Chelsea lapsed back into old habits. Mourinho favors seeing games out after taking leads but, much like Everton's retreat against Arsenal last time out, Chelsea's dropping off played to the Toffees' strengths. They hadn't really tested Thibaut Courtois in any meaningful way but Seamus Coleman's perfect centering feed found the run of Kevin Mirallas and the Blues had their wake-up call.
"I want the team to play the way we did," Mourinho said of what followed. "I want the team to be positive."
The second half had them on the back foot, too, with Everton coming at Chelsea in waves. But the visitors saw it off. Hazard danced away from James McCarthy and the ball was diverted home by the unlucky Coleman. Then the clubs went toe to toe. Naismith got in on the act but it was futile. The more Everton scores, the more Chelsea scores.
Gloss was added by Ramires, who played brilliantly, before Costa ended it in injury time. There were mistakes, there was vulnerability. But unlike Manchester City, whose home loss to Stoke City bore semblance to Chelsea's troubles last season, Mourinho's side had the appetite to add more goals at the other end.
It was a frightening display of power.