The Toffees go into the game in 10th place, but are just four points from fifth, which could yield a Champions League place at the end of the season thanks to Manchester City’s European ban.
A victory in north London could lift them as high as seventh as well as building up a five-point lead ahead of the Gunners.
It would also create a bit of history as Everton have never won at the Emirates and haven’t won away at Arsenal at all since 1996.
Sunday’s game is the first of a crucial four-match period against some of the division’s leading lights that is likely to decide the direction of the rest of the campaign.
This weekend’s meeting is also a tale of two managers who took charge of their respective clubs at the same time but, if rumours are to believed, could have found themselves in the opposite dugout.
Former Toffees Mikel Arteta was heavily linked with a move to Goodison Park while Ancelotti was the supposed experienced head needed to revive Arsenal’s fortunes.
They both watched the reverse meeting at Goodison Park from the stands, but it was Ancelotti who remained on Merseyside while Arteta headed back down to London to replace Unai Emery.
It has been steady if unspectacular progress so far under the Spaniard. They have only lost once under his stewardship but five of his eight Premier League games have been draws.
It means the Gunners go into Sunday’s game in 11th place, the same position they were in going into Arteta’s first game in charge against Bournemouth in December.
That said, a 4-0 thumping of Newcastle and a decent 1-0 victory at Olympiakos in midweek suggests Arteta’s message is getting across as Arsenal look to stay in touch with the increasingly congested group of clubs lurking just outside the top four.
The appointment of Carlo Ancelotti as manager in the morning before kick-off was the only thing exciting about this game, with both sides playing out a dour goalless draw.
Crystal Palace (H) Won 3-1
Watford FC (A) Won 3-2
Newcastle United (H) Drew 2-2
West Ham United (A) Drew 1-1
Brighton (H) Won 1-0
Olympiakos (A - Europa League) Won 1-0
Newcastle (H) Won 4-0
Burnley (A) Drew 0-0
Bournemouth (A - FA Cup fourth round) Won 2-1
Chelsea FC (A) Drew 2-2
Andre Gomes is, remarkably, fit and available to play just 112 days after his horrible ankle injury suffered against Tottenham at the start of November. Ancelotti thinks he is fit enough to start, but will speak to the player before making a final decision.
Bernard is also fit but Theo Walcott faces a late fitness test, with Jean-Philippe Gbamin still out long-term.
What they said
Everton manager Carlo Ancelotti: “We have very important games. Now we have to focus on Arsenal, then we have United, Chelsea and Liverpool.
“After we can see what is going on for Europe [Europa League qualification].
“Sunday is a really important game against a strong team. We are confident and will do our best to try to win.
“Arsenal have improved a lot in the last period, they are trying to play and are better defensively.
“The improvement is clear. They are more confident and it will be difficult.
“But the spirit of our team is good and we are confident, too.”
Everton have worked really hard over the past few weeks to dig themselves out of relegation zone and put them within touching distance of the European places.
Now is the moment they traditionally fall down, but the arrival of Ancelotti needs to coincide with a change in mentality, starting with a confident performance - and - result away at one of the ‘big six’.