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Michael Keane capped another immense performance at the back with the winning goal, rising to meet André Gomes's wicked cross from the left and bury a header past Rui Patricio 13 minutes from time.
That delivery was glanced away by the Wolves defence but was collected by Gomes who swung it back in and Keane did the rest with a well-placed header.
Everton returned to winning ways in the Premier League and moved back into the Champions League spots with a well-earned victory over Wolves at Molineux.
A handball by Doucouré just outside the box had Evertonian hearts in mouths as Neves lined up a direct free-kick but, thankfully, his effort clipped the outside of the post and it was then just a case of Ancelotti's men closing the match out to wrap up another three points.
The result was a triumph for one team playing without a nominal striker against another as Everton lined up without Dominic Calvert-Lewin up front for the first time in the League this season while Wolves continue to operate without Raul Jiminez.
That goal, the England international's third of the season, broke the deadlock of the second half and restored the Toffees' lead which had originally been secured by Alex Iwobi's sixth-minute opener but was then cancelled out eight minutes later by Ruben Neves.
Iwobi found James with a ball inside, the Colombian flighted a cross-field pass to Lucas Digne who volleyed it across the penalty area where Iwobi arrived to side-foot neatly past the keeper.