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Max Kilman's first Wolves goal and Raul Jimenez's 50th were enough to send Bruno Lage's men into seventh place in the Premier League and condemn Everton to a third successive defeat.
Wolves dominated the opening period of an entertaining contest and were worthy of a comfortable half-time cushion provided by Kilman's far-post header and a lovely clipped finish by Jimenez.
However, after being booed off at the break, Rafael Benitez's visitors were much improved when they returned.
Alex Iwobi halved the deficit and it took a fabulous save by Jose Sa to deny substitute Anthony Gordon four minutes from time.
Wolves managed to avoid conceding an injury-time equaliser as they did at Leeds nine days ago to take their points tally to 13 from five games.
For Everton, their second-half improvement was scant consolation as early-season optimism continues to fade for a team yet again mired in mid-table, having now lost the same number of games as they have won.
Raul's got his spark back
It has taken Jimenez a little bit of time to return to his effective best since suffering a fractured skull at Arsenal last season.
But the Mexican was a major threat to Everton.
It was his surging run that ended with Hwang Hee-chan prodding home a goal that was ruled out by VAR and there was no hesitancy about the striker's finish when he capitalised on a Ben Godfrey backpass that managed to perfectly split Mason Holgate and Jordan Pickford.
Jimenez coolly chipped the ball over Pickford, who had already made two fabulous saves to deny Ruben Neves and Francisco Trincao when the game was still goalless.
In front of watching England boss Gareth Southgate, Pickford was earlier beaten when Kilman guided a header across goal and into the far corner.
It was the former England futsal international's first goal as a professional and his celebration underlined the career journey that brought him to Wolves via unglamorous locations such as Maidenhead and Marlow.
More to follow.
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Wolverhampton Wanderers
Squad number1Player nameJosé Sá
Squad number23Player nameKilman
Squad number16Player nameCoady
Squad number27Player nameSaïss
Squad number22Player nameNélson Semedo
Squad number8Player nameRúben Neves
Squad number28Player nameJoão Moutinho
Squad number3Player nameAït-Nouri
Squad number11Player nameTrincão
Squad number26Player nameHwang Hee-Chan
Squad number9Player nameJiménez
Squad number10Player nameDaniel Podence
Squad number17Player nameFábio Silva
Squad number32Player nameDendoncker
Everton
Squad number1Player namePickford
Squad number23Player nameColeman
Squad number5Player nameKeane
Squad number4Player nameHolgate
Squad number22Player nameGodfrey
Squad number14Player nameTownsend
Squad number25Player nameGbamin
Squad number6Player nameAllan
Squad number17Player nameIwobi
Squad number7Player nameRicharlison
Squad number11Player nameGray
Squad number8Player nameDelph
Squad number24Player nameGordon
Squad number33Player nameRondón
Line-ups
Wolves
Formation 3-4-2-1
- 1Malheiro de Sá
- 23Kilman
- 16Coady
- 27Saïss
- 22Nélson Semedo
- 8Neves
- 28João Moutinho
- 3Aït-NouriBooked at 90mins
- 11Machado TrincãoSubstituted forPodenceat 79'minutes
- 26Hwang Hee-ChanSubstituted forFábio Silvaat 90+4'minutes
- 9JiménezSubstituted forDendonckerat 90'minutes
Substitutes
- 2Hoever
- 10Podence
- 15Boly
- 17Fábio Silva
- 21Ruddy
- 32Dendoncker
- 37Traoré
- 39Cundle
- 48Storer
Everton
Formation 4-4-2
- 1Pickford
- 23ColemanBooked at 90mins
- 5Keane
- 4Holgate
- 22Godfrey
- 14Townsend
- 25GbaminSubstituted forDelphat 45'minutes
- 6Allan
- 17IwobiSubstituted forGordonat 78'minutes
- 7Richarlison
- 11GraySubstituted forRondónat 90'minutes
Substitutes
- 2Kenny
- 8Delph
- 15Begovic
- 20Tosun
- 24Gordon
- 26Davies
- 31Lonergan
- 33Rondón
- 64Welch
Live Text
Match ends, Wolverhampton Wanderers 2, Everton 1.
Second Half ends, Wolverhampton Wanderers 2, Everton 1.
Substitution, Wolverhampton Wanderers. Fábio Silva replaces Hwang Hee-Chan.
Rayan Aït-Nouri (Wolverhampton Wanderers) is shown the yellow card.
Séamus Coleman (Everton) is shown the yellow card.
Foul by Hwang Hee-Chan (Wolverhampton Wanderers).
Ben Godfrey (Everton) wins a free kick in the defensive half.
Substitution, Everton. Salomón Rondón replaces Demarai Gray.
Substitution, Wolverhampton Wanderers. Leander Dendoncker replaces Raúl Jiménez.
Hwang Hee-Chan (Wolverhampton Wanderers) wins a free kick in the defensive half.
Foul by Demarai Gray (Everton).
Maximilian Kilman (Wolverhampton Wanderers) wins a free kick in the defensive half.
Foul by Richarlison (Everton).
Attempt saved. Anthony Gordon (Everton) header from the right side of the six yard box is saved in the bottom left corner. Assisted by Andros Townsend with a cross.
Corner, Everton. Conceded by Conor Coady.
Attempt blocked. Séamus Coleman (Everton) right footed shot from the right side of the box is blocked. Assisted by Richarlison.
Rúben Neves (Wolverhampton Wanderers) wins a free kick in the defensive half.
Foul by Richarlison (Everton).
Substitution, Wolverhampton Wanderers. Daniel Podence replaces Trincão.
Substitution, Everton. Anthony Gordon replaces Alex Iwobi.
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