Nuno Espirito Santo's men ran out comfortable 3-0 winners thanks to goals from Raul Jimenez and Leander Dendoncker either side of the interval before Diogo Jota superbly wrapped things up.
Daniel Podence, making his full Premier League debut for Wolves, impressed hugely and won the penalty that Jimenez finished to break the deadlock.
Dendoncker then nodded home Pedro Neto’s free-kick, and Jota made the most of an outstanding Ruben Neves pass.
Wolves are back up to sixth as they await the outcome of Manchester City’s appeal against their two-year Uefa ban, due tomorrow.
We had waited so long to see him in action - and Podence made quite the impression on his first top-flight start.
He was not the only one to catch the eye in this comprehensive win, but he was the one who got Wolves going.
Operating from the left of the front three, the Toffees failed to keep tabs on him throughout.
And the way he won the penalty, which Jimenez duly converted, was a thing of beauty. His fast feet made something out of nothing.
Dendoncker, putting in an attack-minded display, got on the scoresheet while Neves - probably the best player since the league got back going - set up Jota to seal the three points in style.
After drab losses to Arsenal and Sheffield United, this was just what the doctor ordered. The second half was particularly enjoyable to watch.
If they continue like that, they should at least clinch a Europa League berth once again.
The massive piece of team news saw Podence make his full league bow in gold and black, while Neto and Dendoncker also came into the starting XI.
Jota, Adama Traore and Joao Moutinho - who had looked a bit leggy in the previous couple of games, and understandably considering he has now played 57 times for club and country this season - were the ones to drop out.
Everton went with their trusted strike pairing of Richarlison and Dominic Calvert-Lewin, but Wolves had shaken things up significantly in attack.
The hope was to catch the Toffees cold with the unpredictable, 5ft 5in Podence - and he had the game's first shot on target.
Latching onto a nicely-timed through-ball from Romain Saiss, he forced Jordan Pickford into a save down to his left. He did not get the power on the strike he would have wanted, but the intent was good.
Wolves' front three of Podence, Neto and Jimenez seemed pretty fluid in the early going, with the widemen happy to both drop deep and switch sides - keeping Everton, who had Calvert-Lewin shoot straight at Rui Patricio, on their toes.
Lucas Digne then pulled back Neto - trying to break clear, with Jimenez aiming to release him - for what was an obvious booking.
Going into the first-half drinks break, Wolves had looked comfortable enough. They just needed to have a bit more zip and ambition to their play. Podence recognised that, too.
Keen to show why he is the club's third-most expensive signing of all time, the Portuguese played a defence-splitting pass towards Neto - Pickford just about getting there first.
Soon after, Podence wriggled into space inside the box and saw his clever attempt kept out by a sharp Pickford stop.
Jimenez tried something spectacular as well, as his well-executed overhead kick, ultimately, went right into the arms of Pickford.
Despite those encouraging moments, it seemed Wolves' goalless first-half run would continue. However, up stepped Podence, who bamboozled the Toffees backline and won a penalty - kicked on the heel by Digne.
Jimenez coolly did the rest from the spot, sending Pickford the wrong way to, at long last, have a lead heading into the break.
Everton, especially after they lost Yerry Mina to an injury on the half-hour mark, appeared suspect at the back and toothless in attack.
And Wolves doubled their advantage straight after the restart. Neto's inviting, inswinging free-kick from the right was delicately glanced into the far corner by Dendoncker.
The visitors had offered so little all afternoon, and at 2-0, they looked down and out.
Wolves, having had it so easy, still needed to manage the game wisely, though, and not get complacent.
Neto pulled up, unchallenged, and limped off - threatening to upset the home side's momentum. Jota, though, entered the fray, and Nuno's charges continued to turn the screw. The out-of-sync Toffees, meanwhile, made all five substitutions by the hour mark in a desperate effort to salvage something from the game.
Wolves, twice, went ever so close to making it 3-0. Firstly, Podence saw his shot from an acute angle spilled by Pickford and clawed away - just before it crossed the line, with the recently-controversial goalline technology confirming it had not.
A perfectly-weighted Neves through-ball gave Jota a glorious opportunity to score, but the forward fell over.
Thankfully, Jota made no mistake the next time around. Found by another peach of a pass from Neves, he chested the ball down and thumped it past the helpless Pickford to end his drought and put the result beyond any doubt.
Traore and Moutinho also came on as Wolves saw through a much-needed and emphatic triumph with little fuss.
The former prevented further embarrassment for Carlo Ancelotti’s outfit as he, somehow, hit the bar after Jota’s cut-back. Overall, though, a top day for Wolves.
Wolves (3-4-3): Patricio; Boly, Coady (c), Saiss; Doherty, Dendoncker, Neves, Otto; Neto (Jota, 56), Jimenez (Moutinho, 77), Podence (Traore, 70)
Subs not used: Ruddy (gk), Kilman, Vinagre, Buur, Jordao, Gibbs-White
Goals: Jimenez (45+2), Dendoncker (46), Jota (74)
Everton (3-5-2): Pickford; Keane, Mina (Coleman, 31), Digne; Walcott (Bernard, 56), Sigurdsson, Davies, Gordon (Iwobi, 56), Baines (c) (Branthwaite, 46); Richarlison (Kean, 63), Calvert-Lewin
Subs not used: Stekelenburg (gk), Virginia (gk), Sidibe, Baningime
Referee: Anthony Taylor (Manchester)