The Toffees progressed to the final eight courtesy of a 3-0 beating of Burnley in the fourth round, while Marco Silva's charges ran out 3-1 winners over Championship high-flyers Ipswich Town.
Match preview
The fire continues to burn bright within the bellies of Sean Dyche's Everton soldiers, some of whom may still be reeling from their unprecedented 10-point deduction, but they have channelled their anger into something useful with a string of stellar top-flight results.
Having already beaten Nottingham Forest, Newcastle United and Chelsea without conceding a single goal this month, many expected Dyche to mark his return to Turf Moor on Saturday by teaching his old side a footballing lesson, which is exactly what materialised in the evening kickoff.
Amadou Onana's towering header with 19 minutes gone set the Toffees on their way to victory, which ex-Clarets man Michael Keane rubber-stamped with a simple finish at the second bite of the cherry, and the defender did not tone down his celebrations as he boosted Everton's survival hopes at the expense of their lowly hosts.
Burnley boss Vincent Kompany had evidently not learned any lessons from November's 3-0 EFL Cup fourth-round defeat at the hands of Everton, who had previously eked out narrow away wins at Doncaster Rovers and Aston Villa to further their chances of a maiden triumph in the tournament.
The Toffees competed in the quarter-finals two years on the trot in the 2019-20 and 2020-21 campaigns, but Leicester City and Manchester United extinguished their hopes of glory in those years, and not since the 2015-16 season - where they lost to Manchester City in the semi-finals - have they managed to progress to the penultimate hurdle.
After Dyche returned to his old stomping ground to magnificent effect at the weekend, one-time Everton boss Marco Silva will endeavour to follow in his counterpart's footsteps on Tuesday, where the Cottagers could be just 90 minutes away from a first-ever EFL Cup semi-final appearance.
Fresh from successive 5-0 hammerings of West Ham United and Nottingham Forest, in addition to scoring three times against Liverpool and Nottingham Forest, Fulham's newfound Midas touch was not expected to elude them against a Newcastle United side battling injuries, fatigue and European heartache in the wake of their fatal Champions League loss to AC Milan.
However, after Raul Jimenez was given his marching orders for a shocking clattering of Sean Longstaff, Fulham's hopes of a third successive triumph evaporated in a second-half onslaught, where Lewis Miley, Miguel Almiron and Dan Burn condemned the Cottagers to a third defeat in a row on the road.
In fact, not since November's 3-1 beating of Ipswich in the EFL Cup - which succeeded home successes over Tottenham Hotspur and Norwich City - have Silva's men prevailed on their travels, but that success at Portman Road ensured that the Cottagers would post their best result in the tournament for 19 years, having last competed in the quarter-finals all the way back in 2004-05.
Fulham succumbed to a 2-1 loss to West London rivals Chelsea that year, but more recent history favours the capital side, who have achieved three wins and a draw from their last four meetings with Everton, snatching a smash-and-grab 1-0 win at Goodison on the opening day of the 2023-24 Premier League season.
Everton EFL Cup form:
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Fulham EFL Cup form:
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Fulham form (all competitions):
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Team News
A pair of Everton players will return from suspension for the quarter-final, as Idrissa Gueye and Jarrad Branthwaite both served Premier League bans against Burnley at the weekend but are eligible to make their comebacks in the cup.
Vitaliy Mykolenko should also push for a return to the squad after missing the trip to Turf Moor with a "niggle" according to Dyche, but Dele Alli (groin), Andre Gomes (fitness), Ashley Young and Seamus Coleman are all expected to sit this one out.
Dyche was forced into a half-time withdrawal during the win over Burnley, as midfield fulcrum Abdoulaye Doucoure complained of tightness in his hamstring and has now emerged as a doubt for the quarter-final, so the returning Gueye could enjoy an immediate recall to the first XI.
While Everton have two players vacating the naughty step, Fulham striker Jimenez - who was just beginning to revert to his old prolific self - now begins a three-match suspension for his straight red card in the loss to Newcastle, allowing Carlos Vinicius and Rodrigo Muniz to fight for the number nine spot.
Muniz is seemingly winning the striker's battle - having marked a rare start against Ipswich with a goal and also being given the nod ahead of Vinicius for a substitute cameo at the weekend - but Silva could still be without a trio of injury/illness victims.
Calvin Bassey came down with a bug before the weekend and is facing a race against time to prove his fitness for Tuesday, while Adama Traore (hamstring) and Tim Ream (calf) are also expected to remain sidelined for another couple of weeks.
Everton possible starting lineup:
Pickford; Patterson, Tarkowski, Branthwaite, Mykolenko; Harrison, Onana, Gueye, McNeil; Danjuma; Calvert-Lewin
Fulham possible starting lineup:
Rodak; Tete, Adarabioyo, Diop, Robinson; Reed, Palhinha; Iwobi, Pereira, Decordova-Reid; Muniz
We say: Everton 2-1 Fulham
Fulham should not lose their newly-established offensive prowess overnight, but Everton have been the masters of keeping things tight at the back since the start of the month and ought to take advantage of the Cottagers' recent shortcomings on the road.