Despite increasing pressure on Rafa Benitez, the Spaniard watched his side gained their first win in nine matches against Arsenal last Monday, with the winner coming courtesy of Demarai Gray's late strike.
Now the Toffees travel to Crystal Palace, where recent results suggest the Merseysiders should be confident of building some momentum.
They'll also be buoyed by the average form of Patrick Vieira's side, who haven't won in four games.
Best bets for Crystal Palace vs Everton
(All text odds are correct at the time of publication, but the ones in the pretty blue boxes are bang up-to-date)
It doesn't bode well for the Eagles, who are desperate for points having slipped down to 14th in the table with four consecutive games without a win.
Everton also find themselves in the bottom half of the table, but after hovering just above the relegation zone last week, their 2-1 win against Arsenal has seen them climb to 12th.
However, Benitez's side enter the game as 23/10 underdogs, while Palace can be backed to take all the points at 5/4.
Demarai Gray showed again on Monday why his £1.5million transfer fee in the summer was a bargain, scoring his fifth goal of the season in style against the Gunners.
Alongside fellow goalscorer Richarlison, he'll be crucial to Everton's chances again on Sunday, especially as Dominic Calvert-Lewin continues his extended spell on the sidelines.
As for Palace, they'll need their striking department to rediscover their form. Christian Benteke, Conor Gallagher and Wilfried Zaha have all netted four this season, but the Eagles have only managed to find the onion bag once in their last three games.
They will fancy their chances against an Everton side who have conceded a whopping 25 goals this season, but with Sunday's visitors fresh from a win and with an impressive track record behind them, Everton to win and both teams to score is my headline tip.
Last 10 head-to-head record
Crystal Palace wins: 0
Everton wins: 5
Crystal Palace goals: 7
Everton goals: 15
Goals can be found in the second half
As much as both of these teams need points, they'll both also be desperate not to lose. That could make the first half a fairly frosty affair, and both teams' records suggest they open up more after the half-time break.
That's when the goals are likely to come. Out of Everton's 19 goals in the Premier League this season, an astounding 14 of them have come in the second half.
Whether it's a sign of Everton's poor starts or whether Benitez instructs his side to bunker down in the first half is up for debate, but either way it's made for some impressive showings in the second half.
Palace have followed a similar trend under Vieira, and enter Sunday's clash with an identical record of second half goals, scoring 14 of their 19 this season in that period.
It's a pattern that can't be ignored, and so the second half goals market is worth a look - over one goal to be scored after the break is valued at 6/4.
If that doesn't quite cut it, then maybe look towards the second half having more goals than the first - that market is currently valued at 23/20 with Planet Sport Bet.
Value to be found in corners
Another market worthy of your attention on is corners, where stats show that both teams have struggled this season.
Across their 15 games in the Premier League, Palace have averaged just 4.13 corners per game, while Everton are even worse off with just 3.86.
Their numbers leave them ranked 18th and 19th in terms of corners won this season, and with another fairly balanced game expected, it's worth a punt on under 10.5 total corners at 8/13.
Just 46% of Everton's games this season have had over 9.5 total corners, and even then, a majority can be attributed to their opposition.
But with Crystal Palace also lacking in corners, that won't be a threat. Just 53% of Palace's games have had over 9.5 corners.
Goalscorer bets for Crystal Palace vs Everton
In the absence of Calvert-Lewin, Richarlison can be the difference maker for Everton.
The Brazilian was in fine form against Arsenal last week, and but for two very tight VAR calls, he could've had a hat-trick.
In the end he had to settle for just one goal, but that shouldn't distract from how often he found himself in the right place at the right time.
With Cenk Tosun and Salomon Rondon offering very little up top in recent weeks, Richarlison will likely resume his place at the spearhead of Everton's attack, and that only bolsters his chance of finding the net.
In his eight games against Palace, Richarlison has netted twice as well as registering one assist. At 11/5, you can back him to score again on Sunday.
As for Palace, Christian Benteke's record against Everton is eye-catching. Since arriving in the Premier League with Aston Villa, the Belgian forward has played the Toffees 14 times, and scored six goals in those clashes.
The last time he played a full 90 minutes against Everton, he scored for Palace in a 3-1 defeat. As Vieira looks to get his strikers scoring again, Benteke could be a great option as an anytime goalscorer, especially at 2/1.