Everton fought hard against league-leaders Chelsea but Willian’s late deflected strike sneaked a 1-0 win at the death, moments after Gareth Barry had been dismissed for a second yellow card.
Everton gave as good as they got in the capital, with Romelu Lukaku twice being denied by stunning reflex saves from Petr Cech.
Juan Cuadrado, making his first start for Chelsea, looked a threat and the big-money deadline-day recruit dragged a shot wide of the far post, before Tim Howard saved a Loic Remy header in a frantic start.
The lively Eden Hazard went agonisingly close to getting on the end of Cesar Azpilicueta’s fine cross as Everton struggled to contain the leaders, but Chelsea were unable to find the back of the net before the break.
Everton manager Roberto Martinez replaced Muhamed Besic, who was shown an early yellow card, with James McCarthy at half-time and Chelsea were soon back on the front foot after the break.
Hazard was a constant menace to the Everton defence and the Belgium winger fired the ball across the face of the goal, but Bryan Oviedo was well positioned to avert the danger.
The outstanding Hazard then surged into the area, after producing some fine close control, before forcing a save from Howard. The Everton goalkeeper also had to be at his best to save Matic’s well executed free-kick.
The busy Howard again demonstrated why Martinez was so eager to recall him when he produced a diving stop to keep out a measured Willian effort, before Cech showed his class at the other end to thwart an unmarked Lukaku.
Belgium striker Lukaku looked certain to convert Oviedo’s ball in from the left, but Cech stood up to keep out his finish from only six yards out.
Mourinho replaced Cuadrado and Remy with Cesc Fabregas and Didier Drogba 20 minutes from time and Chelsea had a late goal disallowed when Matic’s shot was deflected in off Ivanovic, who was offside.
Barry was then dismissed for a challenge on Willian which sparked a mass confrontation and there was more drama to come, as Howard fisted away a cross into Willian’s path and he rifled home with the aid of a defletion to stun Everton.