Marco Silva hailed "special player" Tosin Adarabioyo after the defender scored the winning spot-kick as Fulham beat Everton on penalties to reach the Carabao Cup semi-finals for the first time.
Centre-back Tosin stepped up in sudden death, after Idrissa Gueye struck the post, and rolled home to send the Cottagers through to a first domestic semi-final in 22 seasons.
Silva's men had a smash-and-grab win at Goodison Park in the opening game of the season and they went home to London victorious once again.
"He is a key player for us, one of the leaders in our dressing room and we need them to step in," said Fulham boss Silva.
"He didn't play the first three months of the season, but he is a special player for us. He can defend the box and on the ball he builds the way I want him to.
"He is getting better and better and a great performance tonight. To be able to take the decisive penalty, he deserves all the credit."
The opener came four minutes before half-time and went down as a Michael Keane own goal, with the Everton defender diverting the ball into his own net from Antonee Robinson's cross.
The hosts could have hit back immediately but James Tarkowski was unable to get enough of a firm connection on James Garner's free-kick and flicked his headed effort narrowly off target.
Everton searched for an equaliser in the second period and Jack Harrison fizzed a long-range drive just wide before substitute Beto headed in from close range with nine minutes remaining.
The game went to penalties, with Bobby De Cordova-Reid seeing his effort saved by Jordan Pickford and Amadou Onana's having a weak effort kept out by Bernd Leno, before Tosin sent the travelling fans into raptures.
The draw for the semi-finals takes place on Wednesday, with the first leg of those ties being played in the week commencing 8 January.
Fulham march on
Fulham have never won a major trophy, but perhaps this could be their time. They reached the FA Cup semi-finals in 2002 when they were knocked out by Chelsea, who are among the teams still left in this competition.
Silva's players battled through the contest with Everton and had only one shot on target, which came in the sixth minute when former Toffee Alex Iwobi's caressed shot was batted out by Pickford.
Former Everton manager Silva said of the hard-fought win: "We are all delighted, no doubt about it. Our aim was clear, to come here and go through. We did it, we knew it would be tough.
"A proper cup tie, but the players kept their composure in the penalty shootout. We achieved something that the club never did in the past."
Keane went from hero to villain, netting an own goal to follow his man-of-the-match performance in Saturday's 2-0 victory at Burnley.
It looked like the hosts were heading out in normal time, but Beto nodded home for the leveller and Arnaut Danjuma could have won it in injury time but sent his sweetly struck volley wide.
Everton had been the better side for much of the encounter - Jarrad Branthwaite, deployed at left-back in the absence of Vitaliy Mykolenko, headed straight at Leno and Dwight McNeil fired over from an acute angle.
But Sean Dyche will be left wondering what might have been on his first appearance in the quarter-finals of this competition as a manager. He watched on as Onana's weak spot-kick to win it was kept out by Fulham's German goalkeeper before Tosin sent the visiting side through.
Despite their 10-point deduction, Everton have been in impressive form in the Premier League, winning their last four games to climb up the table, so this exit will be seen as a missed opportunity to end their long wait for silverware which stretches back to lifting the FA Cup back in 1995.
Dyche said: "It is one of them things, penalties have to be decided some way. I thought the performance was another strong one but we didn't find the true moments of quality in the very end of lots of good moves and getting into good positions.
"If you are brave enough to get up there and take one, you are brave enough to take the consequences. We practise them, they practise them, [coach] Steve Stone did a good job getting it all organised so you do everything you can.
"It is a cup competition. We took the game on, tried everything to take the game. Similar to how we played them in the league, dominated and couldn't find the killer moments. The stadium was great, the fans and everyone took the knocks and got on with it."
