Nuno Espirito Santo's lot were caught napping for both Toffees goals, losing 2-1 and making it five without a win in the top flight.
The unmarked Alex Iwobi put the visitors ahead early on before Wolves levelled swiftly through Ruben Neves and ended the first half strongly.
However, they failed to get going after the break and were punished as Michael Keane emphatically headed home towards the end.
Not the result anyone of a gold and black persuasion wanted going into Saturday's huge clash with Albion.
After keeping Crystal Palace at bay in the FA Cup – ending a 10-game run without a clean sheet – it was hoped Wolves had tightened up defensively.
But lapses in concentration were fatal against Carlo Ancelotti's men, giving them far too much time and space for their two goals.
Nuno's pack were the better side for large parts of the first half and seemed well-placed to really make their presence felt in the second.
The attacks, though, completely dried up. Everton were allowed to regain momentum and eventually got the winner.
Fabio Silva put himself about in the first half but ran out of steam, and so did Morgan Gibbs-White – although that was to be expected. Pedro Neto, taking a heavy whack, tried but without success.
Neves, remarkably grabbing his first goal inside the box from open play for Wolves, did well and was the one attempting to force the issue in the closing stages.
They are lacking at both ends at the minute, though. The forwards are not striking fear into the opposition, and they are conceding soft goals at an alarming rate.
The upcoming Black Country derby means so much and, regardless of the Baggies' struggles, Wolves need to sharpen up.
Adama Traore was not fit enough to be involved after picking up a knock – although Nuno said at the time that it was cramp – in last Friday's third-round win over Palace.
The club decided not to risk the Spaniard, who they expect to be back fit for the much-anticipated encounter against Albion.
It meant Gibbs-White was in from the off, although the midfielder is feeling his way back to full sharpness following his recall from Swansea last week.
Rui Patricio, as expected, replaced John Ruddy between the sticks while 18-year-old centre-half Nigel Lonwijk was on a very youthful bench.
Everton did not have a recognised centre forward in the starting line-up with top scorer Dominic Calvert-Lewin ruled out while both Richarlison and Cenk Tosun were among the substitutes.
They still took the lead after just six minutes, though, thanks to some shoddy Wolves defending.
Iwobi was left completely free on the edge of the box, and he firmly took advantage as he side-footed the ball into the bottom corner.
It was a decent play from the Toffees and Iwobi still had a fair bit to do but, ultimately, his run was not tracked. Soft.
Thankfully, it did not take Nuno's pack long to respond. Picking up the loose ball after Neto's corner, Rayan Ait-Nouri left Abdoulaye Doucoure for dust before firing across goal and leaving Neves with a simple finish from close range.
Excellent work from the young full-back, with Neves finally adding a tap-in to his long list of screamers for Wolves.
From there, the hosts seemed more confident. Gibbs-White was moving the ball with greater urgency than he has tended to in the past, looking sharp considering he spent the last few months of 2020 on the sidelines with a foot injury.
Silva also appeared hungry – in a fluid front three – and was unlucky not to score, seeing his low drive from Neto's low cross kept out by Jordan Pickford.
Neves also had an attempt from trademark range pushed out for a corner by Pickford while Leander Dendoncker steered an effort wide after more impressive stuff on the front foot from Ait-Nouri.
Bouncing back after a sloppy start, it was a pretty solid first half from Wolves – although Iwobi went close again after linking up nicely with James Rodriguez, who was finding pockets of space between the lines for Everton.
Shortly into the second period, Nuno had a heart-in-mouth moment when Nelson Semedo did superbly to evade a crowd of blue shirts and release Neto, who was hacked to the ground by Doucoure.
The Portuguese winger stayed down for a few minutes and once back on his feet, was not moving all that freely. Already having Traore, Willy Boly, Daniel Podence, Fernando Marcal, Jonny Castro Otto and Raul Jimenez nursing various injuries, he could ill afford another one.
Neto, fortunately, was able to continue – albeit with a slight hobble. The game then lost its intensity, with neither side creating any notable opportunities.
Wolves made their first change shortly after the hour mark in a bid to regain their attacking edge as Ki-Jana Hoever replaced Gibbs-White. The Dutchman, a full-back by trade, went to the right of the front three. Patrick Cutrone also came on for Silva through the middle.
But it was the Toffees who regained their spark and grabbed a winner.
Not long after Conor Coady denied Iwobi with a brilliant last-ditch block, Keane rose highest in a crowded box and powered his header beyond the helpless Patricio.
And despite the best attempts of Neves late on – a volley sailing narrowly wide and free-kick grazing the woodwork – that proved to be the winner.
Wolves (4-3-3): Patricio; Semedo, Coady, Saiss, Ait-Nouri; Neves, Dendoncker, Moutinho (Vitinha, 86); Gibbs-White (Hoever, 64), Silva (Cutrone, 78), Neto
Subs not used: Ruddy (gk), Kilman, Richards, Lonwijk, Shabani, Corbeanu
Goal: Neves (15)
Everton (4-4-2): Pickford; Holgate, Mina, Keane, Godfrey; Iwobi, Davies (Gomes, 64), Doucoure, Digne; Rodriguez (Coleman, 86), Sigurdsson (Richarlison, 76)
Subs not used: Olsen (gk), Kenny, Nkounkou, Bernard, Gordon, Tosun
Goals: Iwobi (6), Keane (77)
Referee: Martin Atkinson (Leeds)