A win on Sunday would ensure David Moyes's side could not be overtaken by Liverpool, although victory in itself would be an achievement as they have not come back from the red side of town with three points for 14 years.
After last season's seventh to Liverpool's eighth, Everton would be guaranteed at least a sixth-placed finish with a win.
Unfortunately for them, that would still see them miss out on a place in Europe, though they remain with an outside chance of snatching fifth, and entry to the Europa League, and possibly even a top four champions League berth.
"We'll go there full of the confidence that we've got this year," Everton midfielder Leon Osman told the Liverpool Echo.
"We're five points above them at the minute and a win would certainly be great for us. But we're still on the coat-tails of the teams above us and we're trying to win for that reason as well."
While the European battle is a major focus, for many Everton fans the chance for the right to crow about back-to-back higher finishes is an even tastier prospect.
The fact it has taken so long, despite Everton winning the league five times in the period, points to their inconsistency, illustrated perfectly when they followed their 1970 championship-winning season by finishing 14th.
The few years when the clubs did not play in the same division are not counted in the run but there is still a long period where Liverpool can claim to have had the upper hand.
After being the dominant force in the English game in the late 1970s and 1980s, Liverpool briefly ceded power to their neighbours.
Yet even though Everton won the league in 1985 and '87 - with Liverpool second both times - Liverpool took the honours in between, rubbing it in by completing the 1986 double by beating league runners-up Everton in the FA Cup final.
But where Liverpool have managed back-to-back titles several times over the decades, Everton have never strung two together in the nine times they have been English champions.
It is perhaps therefore telling that they are on the cusp of ending this 76-year wait under a manager whose name is uttered in the same sentence as consistency as much as gritty and sometimes boring.
Moyes has been in the Goodison Park hot seat since 2002, making him the third-longest serving in the Premier League behind Manchester United's Alex Ferguson and Arsenal's Arsene Wenger.
The Scot, whose contract expires this summer, has won admirers for building a competitive team on a limited budget and by the end of this season will have led Everton to seven successive top-half finishes and nine in total.
Critics point to a lack of silverware as a shortcoming in this period of stability, with defeat in the 2009 FA Cup final the closest they have home to a trophy, and a lack of thrills.
While they have enjoyed being something of a bogey team for the bigger teams, with a 4-4 and 3-3 draws against Manchester United and two league victories over them in the past four seasons, some moments on the big stage have been less inspired.
In the FA Cup final against Chelsea four years ago, they took an exciting first-minute lead before shutting up shop and losing 2-1, while in the semi-final against Manchester United they went through on penalties after a drab 0-0 draw then lost to Liverpool in the semis last year.
The likes of Marouane Fellaini and Steven Pienaar have injected class into the team but there remains an overriding sense Everton are not fulfilling their promise when it counts - this year's 3-0 home FA Cup quarter-final defeat by Wigan Athletic a case in point.
They make the short trip to Anfield at their defensive best, however, having kept five clean sheets in seven games, which is ideal form in which to face a Liverpool who thumped Newcastle United 6-0 last weekend.
Liverpool, without their top scorer Luis Suarez who is serving a 10-game ban for biting Chelsea's Branislav Ivanovic, showed they can find goals from elsewhere in his absence and will be motivated to try to close the gap on Everton.
"We still have a chance of catching Everton and that's our target," Lucas, whose side are seventh with 54 points to Everton's 59 with three games to play, said in the Echo.
"We know we have to win if we want to finish a position higher than we are now. — Reuters