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Stewards in high-vis jackets tried to capture the feline who roamed onto the field with 20 minutes remaining of the game.
Staff eventually shepherded the cat off the grass and away from the play to allow the match to resume.
But the Goodison faithful may well have seen it as symbolic as pressure grows on boss Marco Silva grows.
Defeat to newly-promoted Wolves sees Everton drop to ninth in the Premier League with their 10th loss of the season.
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And it came after Toffees were humiliated by Millwall in the FA Cup last weekend.
Wolves made a confident start and silenced the home fans with a seventh-minute opener from the penalty spot.
Leighton Baines made a horrible mess of his challenge on Matt Doherty and clipped the Wolves defender.
Referee Lee Mason didn't hesitate to point to the penalty spot and there were no complaints from Everton's players.
Ruben Neves stepped up to take the kick and dispatched it into the bottom right corner, with Jordan Pickford diving the wrong way.