The hosts fell to a surprise defeat at newly-promoted Aston Villa in their last league outing, whereas Wolves remain unbeaten across all competitions following their Europa League progress on Thursday night.
With the gap between top six and the chasing pack expected to be closer this season than last, matches like Sunday's could be crucial in determining which of the contenders could possibly upset the big boys.
Wolves were the closest last season courtesy of their seventh-place finish, which was enough for them to enter the Europa League qualifiers and subsequently book their place in the competition proper with an impressive 5-3 aggregate victory over Torino in the playoff.
Nuno Espirito Santo's side have since been rewarded with a group including Besiktas, Braga and Slovan Bratislava, but for now focus must turn to claiming their first Premier League win of the campaign.
Three consecutive draws - against Leicester City, Manchester United and Burnley - have left them 15th in the embryonic Premier League table and only one point clear of the relegation zone, and another stalemate this weekend would see them begin a campaign with four successive draws for only the second time, alongside 1938-39.
Despite the obvious desire to get that first win on the board, Nuno may feel that a point away to Everton is not a bad result, having secured the same against another top-six hopeful in Leicester on the opening day.
Wolves have only won one league away game since their last visit here in February, though, picking up just six points from their last eight such outings and failing to score in half of those.
Not since 1960 have Everton lost back-to-back home league games against Wolves and, considering their recent defensive record at Goodison Park, they will be confident of forcing another blank for Nuno's side on their travels.
The Toffees have kept clean sheets in each of their last six top-flight home outings - their longest run since seven in a row in September 2013 - while their league matches this season have seen a division-low three goals.
Everton boast the best defence after three games of the campaign, although both of the goals they conceded came in their most recent league outing as they succumbed to Aston Villa's first triumph since winning promotion.
Marco Silva's side are also the joint-lowest scorers with just one goal to their name so far, and while time must be allowed for new signings to settle in, fans will also want to see big-money summer arrivals like Moise Kean and Alex Iwobi begin to make more of an impact soon.
In fairness, that was the case in midweek as Everton hit four past Lincoln City to book their place in the third round of the EFL Cup, with Iwobi among the scorers and Kean hitting the woodwork.
It was by no means as comfortable a win as the scoreline suggests, though, with Everton needing two goals in the final 10 minutes to finally dispatch of their League One opponents.
Wolves will undoubtedly provide a sterner test, but the Toffees are on a five-match winning run at home in the league, including victories over Chelsea, Arsenal and Manchester United, so will be confident of another three points this weekend.
Everton form: DWLW
Wolves form: DWDWDW
Everton have been hit by the news that summer signing Jean-Philippe Gbamin will miss at least eight weeks due to a quadriceps problem.
A fellow new recruit Jonas Lossl is ready to return from a calf strain, although Jordan Pickford will start in goal as he looks to equal Ali Al-Habsi's Premier League record of playing the full 90 minutes in all 111 of his appearances in the competition.
There is also a decision to be made up front, with Dominic Calvert-Lewin pushing for a start ahead of Kean, who made his full debut in midweek.
Nuno rarely tinkers too much with his starting XI, even with the dual demands of Europa League and Premier League, although there is a slight concern over the fitness of Leander Dendoncker, who scored the winner against Torino in midweek.
Matt Doherty is still working his way back up to full fitness after missing much of pre-season, but he could be one of the players to return this weekend, alongside Ruben Neves and possibly Ryan Bennett.
Everton possible starting lineup:
Pickford; Coleman, Keane, Mina, Digne; Schneiderlin, Gomes; Richarlison, Sigurdsson, Bernard; Kean
Wolves possible starting lineup:
Patricio; Vallejo, Coady, Boly; Doherty, Dendoncker, Neves, Moutinho, Jonny; Jimenez, Jota
We say: Everton 2-1 Wolves
Nuno has won all three of his previous meetings against Silva as a manager, but we see that run coming to an end this weekend. Everton are in flying form at home, while the visitors have struggled to pick up wins on the road recently. Wolves do have enough firepower to breach the Everton's proud defence, but it may not be enough to get anything from the game.