The visitors took an early lead through Beto, who ghosted in at the far post to silence Molineux.
But Hwang Hee-chan’s smart finish dragged Wolves level.
The hosts were struggling to defend the far post and the Toffees took advantage again when Iliman Ndiaye restored their lead.
Kiernan Dewsbury-Hall extended it in the second half with a stunning finish as Wolves offered little going forward.
Rodrigo Gomes pulled a late goal back but Wolves were unable to find an equaliser as they were condemned to another defeat.
Analysis
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Vitor Pereira made five changes to the Wolves team that lost to Bournemouth in their last Premier League game.
Santi Bueno, Jackson Tchatchoua, Hugo Bueno, Andre and Hwang all came in as Matt Doherty, Ki-Jana Hoever, David Moller Wolfe, Jean-Ricner Bellegarde and Jorgen Strand Larsen missed out.
Hoever was not involved due to a knee injury, while Larsen had an achilles knock, but the striker is also keen on a move to Newcastle United amid their ongoing interest.
Wolves’ newest signing Ladislav Krejci was named on the bench.
Everton made a strong start to the game by controlling possession and pressuring Wolves with crosses and set pieces, with the hosts’ defence looking weak on every attack.
Hugo Bueno (Photo by Wolverhampton Wanderers FC/Wolves via Getty Images)
And it took just seven minutes for the Toffees to take the lead. A cross into the box was headed back across goal by Jack Grealish and Beto was left free by Emmanuel Agbadou and Toti Gomes to head home from close range.
The home fans were already becoming increasingly frustrated as Wolves struggled for any creativity or impact up front.
At the back, Beto looked like he was through on goal until S.Bueno made a superb recovery tackle in the box.
Wolves then created a chance from nothing in the 21st minute and scored from their first opportunity.
Marshall Munetsi put in a fantastic cross behind the defence and Hwang was quickest to it to fire into the roof of the net.
The fans were buoyed by the goal and the players began to fly into some tackles, which prompted Pereira to engage from the dugout and demand more aggression. Everton’s James Garner did not like what he saw and he almost squared up with the Wolves head coach.
The hosts then won a corner and Agbadou came close with a hooked shot that flew over the bar.
Jose Sa made a huge save to deny Grealish but Joao Gomes failed to clear his lines, which resulted in Everton’s second.
Grealish’s reverse pass found Dewsbury-Hall, who put in a cross to find Ndiaye at the far post, who had an easy finish after he got away from H.Bueno.
Wolves entered the break losing 2-1.
As the second half got under way, Ndiaye had the ball in the back of the net after Andre lost it needlessly in midfield, but he was flagged offside.
Wolves were looking after possession relatively well, but conceded a third in the 55th minute with another mistake from defence.
Hee Chan Hwang(Photo by Wolverhampton Wanderers FC/Wolves via Getty Images)
This time Agbadou’s terrible pass relinquished possession and Grealish released Dewsbury-Hall, who smashed the ball in off the underside of the bar from a tight angle.
Wolves’ performance was abject in the minutes that followed and the fans began to chant against chairman Jeff Shi and owners Fosun.
On the pitch, H.Bueno went down under a challenge from Ndiaye and was calling for a penalty, but the officials were unmoved.
Wolves were offering little going forward but were given a lifeline when they pulled a goal from nowhere.
Munetsi played a ball to his left for Wolfe, who hit an early cross, and R.Gomes did brilliantly to arrive late in the box and smash the ball into the roof of the net.
Wolves were back on top again and the fans were willing them on - as Pereira and his assistant Luis Miguel conducted the atmosphere from the sidelines.
In six minutes of added time Wolves created a chance when Bellegarde forced a save with a shot from distance, but R.Gomes hit the rebound wide.
And that was their last opportunity as they fell to defeat at Molineux.
Key Moments
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GOAL 7 Beto heads Everton into the lead
GOAL 21 Hwang fires Wolves level
GOAL 33 Ndiaye restores Everton’s lead
GOAL 55 Dewsbury-Hall smashes home Everton’s third
GOAL 79 R.Gomes pulls a goal back for Wolves
Teams
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Wolves: Sa, Tchatchoua (R.Gomes, 64), S.Bueno, Agbadou, Toti, H.Bueno (Wolfe, 75), Andre (Bellegarde, 64), J.Gomes, Munetsi, Arias (Lopez, 64), Hwang (Kalajdzic, 75).
Subs not used: Johnstone, Doherty, Mosquera, Krejci.
Everton: Pickford, O’Brien, Tarkowski, Keane, Mykolenko, Gueye (Iroebunam, 75), Garner, Ndiaye (Coleman, 95), Dewsbury-Hall, Grealish (Alcaraz, 88), Beto (Barry, 75).
Subs not used: Travers, Armstrong, Onyango, Dibling, McNeil.