Everton had more ball possession but substitute Sasa Kalajdzic’s 87th minute winner gave Wolves their first win of the season.
Wolves failed to find a shot on target in the first half and thought they had broken the deadlock after half-time, the goal was ruled out for offside.
Fabio Silver had another clear-cut opportunity after Everton’s defensive mistake, but he ran through and struck wide of goal.
Everton scored their goal in the 79th minute when Doucoure slotted in to finish off a fine move, but the goal was also ruled out for offside.
The West Midlands side have suffered upheaval over the summer, with manager Julen Lopetgui being replaced by Gary O’Neil just a few days before the opening game and star players such as captain Ruben Neves, Joao Moutinho, and Raul Jimenez all departing.
Sasa Kalajdzic, who joined Wolves at the start of last season, but had been pipped with injuries leaped above Nathan Patterson to head home from Pedro Neto’s cross.
There were boos at the final whistle as the hosts remained in search of their first point and goal of the campaign.
Everton now faces another monumental contest at Sheffield United next Saturday.