Michael Keane's second-half header was the winner, after Alex Iwobi had put the Toffees ahead in the sixth minute.
Wolves equalised through Ruben Neves, but they couldn't find another equaliser in the latter stages.
Here are the player ratings:
Rui Patricio- 6/10: There wasn't much he could do for Iwobi's opener as Coady was blocking his view. Wasn't forced into much apart from the two goals and continued his impressive distribution. Keane's winner was too close and too powerful to deal with for him.
Nelson Semedo- 5/10: Caught napping at the back post for Iwobi's goal and often left Lucas Digne free. He did seem to improve once Hoever was introduced, but he continued to give the ball away needlessly.
Conor Coady- 6/10: Another commanding performance on the right of the two centre-backs. Himself and Saiss seem to be developing a solid relationship at the moment, which was helped by the absence of Dominic Calvert-Lewin.
Romain Saiss- 6/10: The midfield turned defender, like Coady, remained solid throughout the evening. Will be disappointed to see Keane find the space inside the penalty area for the winner and his presence within offensive penalty area seems to have died down.
Rayan Ait-Nouri- 6.5/10: Showed glimpses of why Wolves showed interest early on, teasing Mason Holgate when attacking and skimming past Abdoulaye Doucoure for Neves' goal. Was caught out of possession to allow Iwobi space to drive, but offered options going forward.
Joao Moutinho- 6/10: Was better tonight than he was on Friday. Took the majority of Wolves' set-pieces, despite them being short, and sat the deepest of the three midfielders. Was tidy in midfield, but spurred the chance to shoot on a number of occasions.
Ruben Neves- 7/10: Scored his second Premier League goal in a row after finding himself in the box from a corner. Was often chasing Gylfi Sigurdsson into the area and he managed to keep the Iceland international quiet. Was unlucky not to equalise for the second time with a dangerous free-kick.
Leander Dendoncker- 6/10: Squandered two chances in the second half, but his presence in the midfield is certainly showing after time on the sidelines.
Morgan Gibbs-White- 6.5/10: Arguably Wolves' best player. The game was Gibbs-White first start since the start of October for Swansea City and it was impossible to tell. The Wolves' academy product played in a number of roles, including the number 10, false nine and central midfield.
Fabio Silva- 5/10: Was very unlucky not to grab a goal in the first half, only for Jordan Pickford to deny him with a smart save. His passing was disappointing but the effort is certainly there by the striker. With Cutrone back, he could be dropped to the bench at the weekend.
Pedro Neto- 7/10: By far Wolves' most dangerous player. With the absence of Adama Traore, Neto was handed a free role as Nuno Espirito Santo opted for a 4-3-1-2 formation. Whenever he received the ball, he looked set to drive at the Everton defence.
Ki-Jana Hoever- 5/10: Was put out wide on right-wing in-front of Semedo and it was clear that it is not his ideal position. Despite that, the Dutchman did well and caused Everton's problems. Did seem to lack confidence and received a pointless yellow card late on.
Patrick Cutrone- 5/10: Like Friday, wasn't on the pitch for long enough to be handed a fair rating. A starting place on Saturday could be on the cards against a slow West Brom defence.