Wolves moved off the bottom of the league after Rayan Ait-Nouri scored a last-minute winner.
Wolves fell behind early in Julen Lopetegui's first league match in charge of the club when Yerry Mina glanced a corner into the net.
They took the lead midway through the first period from a well-executed corner routine with Daniel Podence calmly sliding the ball past home goalkeeper Jordan Pickford.
It was an entertaining encounter but one in which the attacking weaknesses of both sides were brought to the fore.
The hosts should have regained the lead thanks to Gueye's pass to Anthony Gordon, but he was denied by Wolves goalkeeper Jose Sa.
Wolves forward Diego Costa was unable to get enough power on a diving head to beat Pickford, who also repelled Hugo Bueno's attempt after the break.
In the 95th minute, Ait-Nouri turned the ball past Pickford after being set up by Adama Traore.
The win moved Wolves up to 18th place, which is currently occupied byEverton who have lost four games in a row.
In recent times, there has been a familiar feeling of frustration among fans of the club who are unhappy with the lack of progress on the pitch.
The sight of a manager under pressure is something that seems to be playing on a loop at Goodison Park, with this defeat met by a chorus of boos.
Frank Lampard's team have only won one of their past eight top-flight matches and even though they established an early advantage they never looked in control.
Prior to and after Mina's goal, it was Wolves that looked like they were in control.
There was an element of inevitability about the way things unfolded, withEverton, who have the second worst record in front of goal at home in the premier league, failing to make the most of their chances and then succumbing to a late Wolves counter- attack.
There's more to come.
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