All the frantic action happened in the final 13 minutes with Chelsea striker Diego Costa and Everton midfielder Gareth Barry sent off but their dismissals only came after Lukaku's brilliance had put the tie beyond doubt.
The powerful Belgium striker, who never fitted in at Stamford Bridge and was sold to the Merseysiders for 28 million pounds two years ago, proved irresistible with his late five-minute double, especially with a first goal destined to go down in Goodison Park folklore.
As the game meandered towards a replay, Lukaku conjured a 77th-minute goal from nowhere, muscling past two defenders on the left, powering into the box and, after some nifty footwork to bamboozle Gary Cahill, firing in a left-foot effort.
Everton manager Roberto Martinez hailed it "one of the great goals we will see in the FA Cup".
Five minutes later, freed by Ross Barkley's neat pass, the 22-year-old Lukaku shot through keeper Thibaut Courtois' legs to provide the perfect response to any notion that he was not good enough for Chelsea.
"I don't think I have anything to prove to Chelsea. I went there as an 18-year-old and learned the trade of being a professional. I will always be grateful to them," Lukaku told the BBC after taking his goal tally for the season to 25 in all competitions.
"I think the first goal is the best thing. I didn't know where I was going but then I was in the box, I saw Gary Cahill not know where he was going so I shifted it on to my left foot."
What irony, though, that a Chelsea reject's goals should end a thoroughly wretched week and, effectively, put the lid on a terrible season for the Premier League champions following their Champions League exit to Paris St Germain on Wednesday.
Moments after Lukaku demonstrated his excellence, Chelsea target man Costa could only offer up another striking example of his pointless 'angry young man' impressions.
This time, after an earlier first-half booking for a collision with Barry, he squared up to the midfielder, shoving his face into the Everton player after being fouled.
For a moment it even looked as if he was burrowing into Barry's shoulder with his teeth but the former England international's calm reaction betrayed no sign he had been bitten.
Either way, referee Michael Oliver felt his petulant response meant he had to go for a second yellow card offence, surprisingly the first time he has been sent off for Chelsea.
Soon after, sparring partner Barry was also dismissed for a second booking for a foul on Cesc Fabregas.
The defeat meant caretaker manager Guus Hiddink, who won the FA Cup seven years ago in his previous stand-in spell at Stamford Bridge, had failed in his bid to repeat the achievement following the dismissal of Jose Mourinho in December.
In a game high on spikiness and huff and puff but not an abundance of great skill until Lukaku took over, the best chance fell to Costa who rounded keeper Joel Robles only to see his shot skip across the face of goal millimetres from the line.
A trip to Wembley for the semi-finals represented the perfect welcome gift for Everton's new principal shareholder Farhad Moshiri.
"I am the one bringing expectation and every single player at the club has the right mental character," said Martinez. "We wanted to get to Wembley and our chairman (long-standing owner Bill Kenwright) deserves that for what he has achieved."
