The Toffees took the lead early in the second half as Gylfi Sigurdsson's corner was headed in by Richarlison, who notched his first goal in 12 games in front of a delirious Gwladys Street End.
Should Everton better Tottenham Hotspur's result on the final day on Sunday, they will play European football for the first time since 2017.
Story of the match
Carlo Ancelotti made two alterations to the side defeated by Sheffield United on Sunday as Yerry Mina and Gylfi Sigurdsson came in, while Nuno Espirito Santo made five changes from the loss against Tottenham, which included John Ruddy's first Premier League start since March 2019.
In a first half of little goalmouth action, the visitors were largely dominant. It took 11 minutes for the game's first attempt, as a Richarlison header went straight down the throat of Ruddy. Shortly after Wolves went close, as Morgan Gibbs-White's impressive volley from 25 yards was pushed wide by Jordan Pickford.
Wolves then enjoyed a lengthy spell of dominance that resulted in a couple of half chances. Firstly, Fabio Silva's attempt on the turn was deflected over the crossbar by Mina, and Adama Traore's attempt from the resulting corner was tipped over by Pickford. Traore was by far the most lively player in the first half and caused the Everton backline huge concern.
Despite their lack of possession and chances, Everton ended the half the stronger and had their best chance just before the interval. Lucas Digne's delicious inswinging corner fell to the feet of Richarlison inside the six yard box, but Nelson Semedo got back in the nick of time to divert the Brazilian's effort wide.
While Richarlison couldn't convert from Everton's last corner of the first half, he did from their first of the second. Sigurdsson's brilliant delivery was glanced in off the far post with ease by the former Watford man as Wolves' set-piece weakness continued to show. The hosts were all over Nuno's side immediately after the goal, and could have doubled their lead as Conor Coady deflected Seamus Coleman's effort just wide.
Wolves then had their first attempt of the second 45 as Traore beat three players before firing straight at Pickford, but the visitors couldn't produce any real pressure after falling behind. After a lull in the game around the hour mark Dominic Calvert-Lewin had the opportunity to double Everton's lead after going through on goal, but his effort at an angle was saved by Ruddy.
Sigurdsson almost added a goal to his assist as his curling effort from distance hit the stantion behind the Gwladys Street goal, before late Wolves penalty claims were waved away by both Andy Madley and VAR after a Traore cross hit the hand of Abdoulaye Doucoure.
Keane and Godfrey impress in front of watching Southgate
With just six days to go until England's squad for Euro 2020 is revealed, Everton's defensive pair of Michael Keane and Ben Godfrey staked a last minute claim for a place in the 26 in front of the watching Gareth Southgate.
Although the Toffees were facing one of the league's most tepid attacks, both Keane and Godfrey coped brilliantly with the threat of Traore, with the former's tackle on the Spaniard after impressively keeping up with him on the right-hand side certain to have impressed the England manager.
With Harry Maguire's injury and the worrying form of Conor Coady, Tyrone Mings and Eric Dier, one of the Everton duo should fancy their chances of wearing the Three Lions on their chest in June.