Match ends, Everton 2, Chelsea 0.
Everton 2-0 Chelsea
Chelsea striker Diego Costa was at the centre of a biting controversy as Romelu Lukaku wrecked what was left of his former club's season to secure Everton's place in the FA Cup semi-finals at Wembley.
Costa appeared to make contact with the neck of Everton's Gareth Barry at the end of a running battle between the pair as he received his first red card in English football - although managers Guus Hiddink and Roberto Martinez later refused to condemn the striker.
Everton were leading through Lukaku's superb 77th-minute solo goal - reminiscent of Ricky Villa's famous weaving run for Spurs in the 1981 FA Cup final against Manchester City - and the Belgian's low drive when Costa was dismissed by referee Michael Oliver.
It was Lukaku's brilliance which decided this stormy quarter-final - and there was still time for Barry to be sent off after receiving a second yellow card for a foul on Cesc Fabregas.
That could not stop the elation sweeping around an ecstatic Goodison Park as manager Martinez, under the watchful eye of Everton's new majority shareholder Farhad Moshiri, celebrated a hugely significant victory.
Lukaku's touch of class
This was the day Chelsea would have had to acknowledge the error of their ways for their lack of patience in refusing to persist with Lukaku, 22, who is now approaching world class.
He has scored 25 goals this season and the goal that changed the direction of this feisty FA Cup tie was a thing of power and beauty.
Lukaku picked up Ross Barkley's pass on the left flank and embarked on a run that simply possessed too much power and skill for four Chelsea defenders before he had the composure to slide a finish under Thibaut Courtois.
And as Chelsea now look at a major rebuilding job under owner Roman Abramovich's next managerial appointment, how they must wish they had a player of Lukaku's potential to act as the centrepiece.
As for Everton, the fact they do have the giant Belgian means they have a potent match-winning spearhead.
Costa sums up Chelsea's woes
The sight of Costa, with the mockery of almost 40,000 Everton fans ringing in his ears, sloping off after a red card encapsulated a week of abject misery for the Stamford Bridge club.
Chelsea were well beaten by Paris St-Germain and now this FA Cup exit means they have nothing left to fight for and no Champions League football to look forward to next season for the first time since Abramovich took charge in July 2003.
It was as if all those frustrations poured out of Costa, who was agitating for a battle from the first whistle and found an opponent in Barry who was more than happy to oblige.
Costa finally boiled over in a close range, head-to-head spat with Barry and Chelsea's chances of getting back into this game went with him.
With a new manager to be appointed, captain John Terry facing an uncertain future, and a squad needing urgent rebuilding, this day almost felt like the end of an era for Chelsea.
Moshiri's first impression
Everton's new majority shareholder Moshiri, who saw his 49.9% stake in the club approved by the Premier League, was attending his first game since effectively taking control of the club.
And while he confirmed the issue of Everton's ground is high on his agenda, he sampled this glorious old arena at its finest - a bear-pit from first to last and resounding to raucous sounds of victory at the final whistle.
In a message in the match programme, Moshiri also revealed he has pledged funds to keep Everton's best players.
What price Lukaku?
Man of the match - Romelu Lukaku
What they said...
Everton boss Roberto Martinez: "My interpretation is I don't think it was a key moment [involving Costa]. It was an emotional game and rightly so.
"Diego Costa had a fighting spirit and I would like to praise the referee. The sending-off of Costa was right.
"The sending-off of Gareth Barry was right and the referee never allowed those emotions to stop the fluency.
"Whatever happens with Diego Costa I am sure the two players shook it off. From where it was he moved his head towards Gareth Barry and I lost sight of that action.
"I thought it was a second yellow. It was a moment that didn't have an impact on the scoreline."
Chelsea boss Guus Hiddink: "I try to be fair in my judgement [on Diego Costa], I haven't seen it and it is difficult for me to say yes or no [if he had bitten Barry].
"He was chased a bit in the game. They went after him. They knew it. It is within the rules.
"I like him still going towards the edge but you also have to take into consideration he was desperate to play today.
"It would have been better to rest him but it is not the type of game you rest players.
"It is all the combination; not fully physically fit and all the provocations and he has to take responsibility for the incident."
The stats you need to know
- Gareth Barry was sent off for the second time this season - he was also red-carded against Chelsea last season.
- The Toffees have reached the FA Cup semi-final for the first time since 2011-12, where they were eliminated by Liverpool.
- Guus Hiddink lost his first FA Cup match as Chelsea manager, having won all six of his games previous to this.
Everton play Arsenal at Goodison Park in the 12:45 GMT kick-off next Saturday, while Chelsea host West Ham in the Premier League on the same day at 15:00 GMT.
- 6JagielkaBooked at 42mins
- 25Funes Mori
- 18BarryBooked at 87mins
- 12LennonSubstituted forStonesat 88'minutes
- 20BarkleySubstituted forBesicat 90+2'minutes
- 10LukakuSubstituted forNiasseat 90+4'minutes
- 16KenedySubstituted forTerryat 85'minutes
- 21MaticSubstituted forRemyat 82'minutes
- 22WillianSubstituted forOscarat 73'minutes
- 4FàbregasBooked at 62mins
- 19Diego CostaBooked at 84mins
- Michael Oliver
- Shots on Target
Second Half ends, Everton 2, Chelsea 0.
Substitution, Everton. Oumar Niasse replaces Romelu Lukaku.
Substitution, Everton. Muhamed Besic replaces Ross Barkley.
Offside, Chelsea. John Obi Mikel tries a through ball, but John Terry is caught offside.
Attempt blocked. Loïc Remy (Chelsea) right footed shot from the centre of the box is blocked. Assisted by Oscar.
Substitution, Everton. John Stones replaces Aaron Lennon.
Second yellow card to Gareth Barry (Everton) for a bad foul.
Cesc Fàbregas (Chelsea) wins a free kick in the defensive half.
Foul by Gareth Barry (Everton).
Pedro (Chelsea) wins a free kick in the defensive half.
Foul by Ross Barkley (Everton).
Substitution, Chelsea. John Terry replaces Kenedy.
Gareth Barry (Everton) is shown the yellow card.
Second yellow card to Diego Costa (Chelsea).
Diego Costa (Chelsea) wins a free kick in the attacking half.
Foul by Gareth Barry (Everton).
Goal! Everton 2, Chelsea 0. Romelu Lukaku (Everton) right footed shot from the right side of the box to the centre of the goal. Assisted by Ross Barkley with a through ball.
Substitution, Chelsea. Loïc Remy replaces Nemanja Matic.
Foul by Gary Cahill (Chelsea).