When history comes to judge this game it will zone in on two minutes either side of half-time.
Carlo Ancelotti had promised changes in personnel for his team's third match in seven days.
He made three of them but surprised everyone with a change of formation, too, Everton lining up with three at the back – including Lucas Digne – and utilising the pair of Theo Walcott and Leighton Baines, both starting for the first time since 1 March, as wing backs.
Manager Ancelotti’s system matched up with his opponents and suffocated the hosts centrally.
Everton’s first-half sights of goal were limited but there wasn’t a lot doing for Wolves either, the home side's brightest moments coming when they worked the ball wide.
For their greater possession, Wolves couldn’t claim to be forcing the issue and we appeared to meandering towards half-time when, for the second game running, Everton conceded a penalty.
But unlike the errant James Ward-Prowse for Southampton on Thursday, Wolves' gun striker Raul Jimenez had his eye in.
The award looked harsh to the naked eye.
Lucas Digne, who had defended excellently to this point, was confronted by Daniel Podence bustling into the box.
Frenchman Digne steadied himself, resisting the urge to lunge at the Wolves attacker.
Podence went over nevertheless and referee Anthony Taylor’s decision to point to the spot was supported by VAR Andre Marriner.
Jimenez rifled to Jordan Pickford’s right to give the home team an advantage they couldn’t have imagined was imminent.
Pickford had made one very good save at this stage – the England keeper applying a strong right hand to turn round Podence’s 25th-minute blast at the near post after the Portuguese progressed into Everton’s box from the left – but you’d have got short odds on the teams going in goalless.
Everton re-emerged for the second half looking very different. Gone was the three-man defence, replaced by a back four, with Digne on the left.
Jarrad Branthwaite, who turned 18 only 15 days ago and was playing his football in League Two for Carlisle United at the start of this year, came on for a debut at centre half.
Before we could see if these changes would influence the narrative Wolves scored again to totally alter the complexion of the game.
Branthwaite’s nudge on Jimenez was penalised and Leander Dendoncker met Pedro Neto’s inswinging free-kick delivery from the right with a glancing header beyond Pickford.
Wolves’ two-goal advantage forced Everton to take chances and Diogo Jota capitalised on additional space and a stunning pass from Ruben Neves to blast home his team’s third with 16 minutes remaining.
Theo Walcott started his first game in 133 days – at right wing-back under an unforgiving sun, to boot – and the former Arsenal player was involved in Everton’s two most promising moments of the opening half.
He threw up his arms to question why there were no takers for a cross begging to be touched home – but the move leading up to Walcott’s delivery is worthy of mention.
Yerry Mina – whose afternoon would last only 31 minutes after he was hurt in the most innocuous circumstances, passing a ball deep in his own penalty box with no one near him – smacked a terrific pass to Walcott.
Tight to the touchline he fed Anthony Gordon who controlled and pirouetted clear of Neves, before finding Gylfi Sigurdsson, who located Walcott’s forward run.
If Everton were forced round the houses in that instance, the visitors were rather more direct after three minutes.
Walcott looked up from deep and spying Dominic Calvert-Lewin on the move bent a fabulous ball for the striker.
The angle was tight for Calvert-Lewin and he tried to strike across Rui Patricio who made the save.
Wolves advanced by similar means 60 seconds earlier, the bright Podence released by Romain Saiss’s straight ball but not asking much of Pickford to save down to his left.
Gordon, on his first Premier League start away from Goodison Park, was buzzing about, taking up positions which made him a nightmare to mark.
When Wolves players did get close to the teenager they were more often than not left trailing by Gordon’s close control and turn of foot.
You rated his chances of hitting the target when he aimed a shot from 20 yards only for Neves, perplexed by that midfield spin from Gordon moments before, to fling himself in the way of the strike.
Wolves’ cavalier wing-back Matt Dohery advanced early on via an exchange of passes with Jimenez but dragged wide.
Digne, who went in the book on 19 minutes for dragging back Neto off the ball, had to get his timing spot on soon after when tackling the same player in the penalty box.
Jimenez’s strike was his 25th in all competitions this season but he was showing he has more in his locker than goals.
A partially cleared corner was helped back into Everton’s box by a combination of Doherty and Willy Boly, finding the Mexican with his back to goal.
He needed two touches to set himself before launching into an overhead kick which forced a smart stop from Pickford.
Anceotti’s tactical overhaul didn’t have time to take shape before Wolves went two in front and Neves thrashed over from distance on Wolves’ next attack.
But Italian Ancleotti continued to pursue a way back for his side.
Off came Gordon and Walcott – after his 500th club appearance in English football – Bernard and Alex Iwobi given 35 minutes each to try to have a say in the game.
Everton, though, were struggling with the devilish task of containing Podence.
Former Olympiakos player Podence wriggled free of Digne and momentarily thought he’d scored when his shot slipped through Pickford’s grasp.
The keeper reacted to drag the ball back from his goalline and deny the forward.
Full-back crossed for full-back when Digne’s delivery was met by Mina's replacement Seamus Coleman with a header which deflected narrowly off target.
But with Everton opening up, Wolves grew as a counter-attacking threat.
A pass from Neves released substitute Jota but he stumbled at a critical moment.
Digne, meanwhile, back at left-back, was showing up as one of Everton’s most notable attacking threats.
He pulled back for Sigurdsson to slam a shot that was blocked by Neves and thudded a drive past the far post after being fed by Michael Keane, albeit the VAR would have been asked to rule had it gone in, with the lineman’s flag raised.
Digne supplied the cross for Calvert-Lewin to leap and bring a save from Patricio, too, but by then Jota had profited from Neves’s glorious pass to put the outcome beyond doubt.
Furious Wolves manager Nuno volleyed a water bottle into the dugout after Jota set up his fellow replacement Adama Traore for what looked like a gimme only for the Spaniard to strike the bar.
This defeat has extinguished Everton's European aspirations and they have only four days to dust themselves off before Aston Villa visit Goodison on Thursday.