While the majority of the Toffees recent trips across Stanley Park have produced few memorable moments, there have still been some notable successes that the blue half of Merseyside have enjoyed in their enemy's backyard.
Here, Sports Mole counts down Everton's five finest Anfield moments.
5. Ending the drought - 2021
After 22 years had passed without Everton winning a single game at Anfield in any competition, some may have started to wonder whether the Toffees had the mental strength to overcome the unwanted streak which lingered over the club like a dark cloud.
A whole generation had grown up without seeing Everton win away at Liverpool, but that first success of the 21st century finally came in February 2021, when Carlo Ancelotti led the blue half to end the Anfield curse.
What made the 2-0 success even more sweet is that Liverpool were the reigning Premier League champions, while Everton's side was much inferior - apart from the glamour of James Rodriguez - and would go on to fight relegation in the following two seasons.
4. Jagielka's sensational strike - 2014
By scoring arguably the fixture's finest ever goal, Phil Jagielka was the unlikeliest last-minute hero when Everton left Anfield with a point in 2014.
After both sides had excellent seasons during 2013-14, the fixture was billed as a potential thriller, but there was not the same fireworks seen when the sides drew 3-3 at Goodison Park 12 months earlier over the 90 minutes.
Steven Gerrard's free kick looked like it was going to be the winner as Liverpool led 1-0 heading into the 92nd minute, but after the Reds failed to properly clear Aiden McGeady's cross, Jagielka fancied his chances and unleashed a truly remarkable half-volley that gave Simon Mignolet no chance, snatching a point for the Toffees from the jaws of defeat.
3. A bittersweet victory - 1986
As reigning First Division champions under Howard Kendall, Everton knew their stiffest competition would come from their city rivals, making the Anfield derby in February 1986 potentially title-deciding.
An error from Bruce Grobbelaar saw Everton lead through Kevin Ratcliffe, before another second-half strike from Gary Lineker - his 30th of that season already - sealed a memorable Anfield win between undoubtedly English football's two finest clubs of the era.
However, despite getting the upper-hand over Liverpool in the title race, surprising late-season defeats to Luton Town and Oxford United saw Everton squander top spot and eventually lose the league by two points to their local rivals.
2. All but clinching the title at Anfield - 1970
With nine games to play of the 1969-70 season, Everton were firmly the challengers and not the pace-setters behind Leeds United at the top, and six of those remaining games would be away from Goodison Park.
However, suddenly, Everton hit a phenomenal run of form, and after winning at Tottenham Hotspur and Stoke City, a trip to Anfield also awaited, and goals from Joe Royle and Alan Whittle sealed a famous and almost title-clinching victory.
Everton continued that momentum to eventually win the title by nine points, thanks to winning eight and drawing one in that difficult-looking nine-game spell to end the season.
1. The start of something special - 1984
Undoubtedly the one Anfield fixture that will stick in the mind of Everton supporters of a certain vintage will be the meeting from October 1984.
The only other strike that can lay claim to be Everton's best-ever derby goal along with Jagielka's came here, thanks to Graeme Sharp's stunning long-distance looping volley in front of the blue contingent behind the goal which proved to be decisive as the Toffees won 1-0 at Anfield.
In what was the first famous win in a long list during the 1984-85 season, Everton went on to be crowned English and UEFA Cup Winners' Cup champions, cruising to the domestic title at a canter, 13 points ahead of Liverpool - during the two-points-per-win era too it must be noted.