The Toffees remain in danger of the drop, but their hopes of survival were boosted when they beat relegation rivals Nottingham Forest 2-0 on home soil last Sunday.
Goals either side of half time from Idrissa Gueye and Dwight McNeil helped Sean Dyche's side claim three valuable points and move five points clear of the bottom three with a game in hand on 18th-placed Luton Town.
Everton, who sit 16th in the table, have collected six points from their last three Premier League fixtures, as many as they mustered in their previous 13 matches combined.
The Toffees have won their last two home league games without reply during this run, and they will aim to come out on top in three consecutive league fixtures at Goodison Park without conceding for the first time since a run of five in 2019 when they play host to city rivals Liverpool on Wednesday.
Everton seeking to end miserable winless home run against Liverpool
However, success in midweek could prove challenging for Everton as they have failed to win any of their last 12 Premier League home matches against Liverpool, losing three and drawing nine.
This run is Everton's longest without a home league win against any team in their history, and Dyche's side must claim maximum points against Jurgen Klopp's men if they wish to avoid extending this miserable streak.
Everton last celebrated a Merseyside derby victory in front of their own fans back in October 2010 under former boss David Moyes when goals from Tim Cahill and Mikel Arteta sealed a 2-0 win.
Goals have been hard to come by for the Toffees this term, with only basement club Sheffield United (31) having scored fewer than Dyche's men (34), and they have also struggled to find the net against Liverpool as they have not scored in any of the last four league Merseyside derbies.
Everton are also without a victory in all eight meetings against teams currently in the top five of the Premier League, losing six and drawing two, and they enter Wednesday's 244th Merseyside derby as huge underdogs against their title-chasing counterparts.
Sean Dyche talks up importance of Merseyside derby
Dyche has encouraged his Everton players to 'win their individual battles' and adopt the right mentality if they wish to come out on top on Wednesday.
"It's an old-fashioned term, but win your headers, win your tackles and win your races," Dyche said at a press conference on Tuesday. "That used to be a big thing when I was playing and it's still kind of there, really. That's your own individual moment in a game when you are dealing with whoever you are playing against.
"That's for every position. You can win your battles in a different way. If you are a centre forward, you might win it with your cleverness, rather than your physicality. So you know there are different ways to win your battles.
"I don't think that goes anywhere other than the start point of a team game. You have to know what your role is against that player, but also your covering role as part of a team unit.
"So, therefore, rather than worry about each battle, there has to also be connectivity with the team. That's where the shape becomes important, the tactics and the delivery of a physical performance to cover the ground needed.
"You want those individual battles for each player to also connect as a team. If you get that right you have a better chance of getting what you want which is to win."
Everton were beaten 2-0 by Liverpool in the reverse fixture at Anfield in October last year; Ashley Young was sent off in the first half before Mohamed Salah scored two second-half goals to secure all three points for the Reds.