Alex Iwobi put the Toffees ahead in the sixth minute prior to Ruben Neves' quick response.
However, the visitors lifted themselves to fourth in the Premier League when Michael Keane's thumping header floated into the net.
Story of the match
Both sides were forced into a formation switch from their normal styles, with Wolves opting for a 4-3-1-2 formation, whilst Everton implemented a back five with Gylfi Sigurdsson their first line of attack with the absence of Dominic Calvert-Lewin.
Carlo Ancelotti's decision to utilise the Icelandic attacking midfielder paid off in the opening stages when Iwobi latched onto Lucas Digne's pull-back to put the Toffees ahead.
Iwobi's goal was his first goal since he netted in the 3-2 win over Wolves early last season.
The goal seemed to wake the home side up, with Neves, Morgan Gibbs-White and Pedro Neto all pulling the strings in a packed midfield.
Their spell of possession paid off when Rayan Ait-Nouri's cross from the byline was trodded him by Neves, his first league goal at Molineux since the 2-1 win over Aston Villa in 2019.
Moments later, Jordan Pickford showed great reactions to deny Fabio Silva of his first Molineux goal with a brilliant low save.
Neto's drive into the penalty area resulted in him finding his way into the Everton penalty area, before pulling the ball back for the teenager, who did everything right before being denied by the English goalkeeper.
The second half started with both side's lacking the cutting edge that was clearly missing from their striker's not on the pitch.
Ancelotti's side restored their lead with over 10 minutes remaining through Keane's third league goal of the campaign.
The original corner evaded everyone before Andre Gomes arrowed the ball into the box for the central defender to head the ball across Rui Patricio and into the net.
Neves nearly equalised for the second time, with his set-piece swinging just too wide, grazing off the post on it's way out.