Sean Dyche's men play earlier than many of the sides fighting relegation with them, meaning a win could give them a psychological edge.
Match preview
In order to gain those three valuable points though, Everton must improve on their last performance when their four-game unbeaten streak came to an end at Old Trafford.
A 2-0 defeat to Manchester United extended an absolutely woeful away record which has seen them win just two of their last 32 away Premier League games.
The absence of Abdoulaye Doucoure was evident in the Everton midfield, as replacing him with Ellis Simms and moving Demarai Gray further back greatly reduced the intensity and energy in the middle of the park.
Erik ten Hag's side were able to cut Everton open at will, drawing nine saves out of Jordan Pickford over the 90 minutes - the second-highest tally of any goalkeeper in a single PL game this season.
It has been a different story on home soil for the blue half of Merseyside under Dyche though, as they have taken 10 points from a possible 15 on offer since the ex-Burnley boss took charge.
Four of the five sides they have faced at Goodison are in the top half as well which makes that record appear even more impressive, with Fulham also entering the weekend in the ninth.
There is increased pressure on this fixture for the hosts though, given how results went against them last weekend, with West Ham United, Bournemouth, Wolverhampton Wanderers and Crystal Palace all winning.
Wins for so many of Everton's direct rivals saw them fall to 17th, only outside the bottom three on goal difference ahead of Nottingham Forest.
Shooting a blank at Old Trafford also saw them return to the bottom of the scoring charts outright again, as their striking woes continue with a dismal 23 goals in 30 games.
However, despite being in trouble near the bottom, Everton's form is nowhere near as concerning as Fulham's.
The Cottagers have fallen off massively after giving themselves a real chance of qualifying for Europe, losing five straight games in all competitions.
Losing to Brentford narrowly, against league leaders Arsenal, and to Manchester United in extraordinary circumstances in the FA Cup were all forgivable, but defeats to Bournemouth and West Ham since the international break have been concerning, especially considering the Hammers lost 5-1 at home to Newcastle United just days prior.
Each defeat leaves their European hopes dangling by a thread as Marco Silva's men are now seven points adrift of the top seven.
Coming to Goodison Park is not the ideal location for them to try to return to form either, given their notoriously poor record at this stadium.
They won 2-0 here behind closed doors in 2021, but before that, they had the longest away winless run any club has had against a single opponent in top-flight history.
A run of 22 consecutive defeats preceded that win in front of an empty Goodison, as they were also winless in 27 visits dating back to 1949.
Manager Silva will also be looking for a first win over Everton - he lost 3-2 here with Watford after being 2-0 up in 2017, with former Everton man Tom Cleverley missing a 101st-minute penalty.
Everton Premier League form:
L
D
W
D
D
L
Fulham Premier League form:
W
D
L
L
L
L
Fulham form (all competitions):
W
L
L
L
L
L
Team News
Dominic Calvert-Lewin has started training on grass again and could be involved in the squad for this one after missing Everton's last nine matches.
That could put both Simms and Gray in danger of dropping to the bench, as Dyche may want to return to a three-in-midfield formation.
Doucoure remains suspended meaning one of James Garner or Tom Davies could come in to play alongside Amadou Onana and Idrissa Gueye in midfield.
Andros Townsend is still out, but Nathan Patterson made his first appearance for the Toffees off the bench last week after three months out.
Aleksandar Mitrovic will continue to serve his lengthy eight-match ban following his sending off against Man United, with Carlos Vinicius expected to deputise again up front.
Willian returned last weekend from his ban following the United debacle, and he was arguably Fulham's best player despite defeat against West Ham.
Kenny Tete and Issa Diop could reclaim their places in Fulham's back four after the pair dropped to bench for Cedric Soares and Tosin Adarabioyo at Craven Cottage last Saturday.
Layvin Kurzawa and Neeskens Kebano remain on the absentee list for the visitors.
Everton possible starting lineup:
Pickford; Coleman, Keane, Tarkowski, Godfrey; Iwobi, Onana, Gueye, Garner, McNeil; Gray
Fulham possible starting lineup:
Leno; Tete, Ream, Diop, Robinson; Reed, Palhinha, Decordova-Reid, Andreas Pereira, Willian; Carlos Vinicius
We say: Everton 1-1 Fulham
Despite their superb home record against Fulham, Everton are on a dreadful run of results against newly-promoted sides, not winning any of their last nine.