The result lifts Sean Dyche's men to 15th in the table with 14 points, five clear of 18th-placed Ipswich Town, while Wolves remain in the bottom three, sitting second from bottom with just nine points from 14 matches.
After four matches without a goal, it took Everton just 10 minutes to end their drought when Ashley Young superbly curled a free kick from just outside the area into the bottom right corner, marking the 39-year-old's 50th Premier League goal and a fantastic start for the Toffees.
Six minutes later and Everton thought they had doubled their lead through James Tarkowski's header, but celebrations were brought to an end with the news of an ongoing VAR check, with the goal eventually ruled out for offside against Orel Mangala, who was controversially judged to have interfered with play.
The Toffees were not to be denied a second time, doubling their lead just after the half-hour mark when Mangala redeemed himself for being caught offside in the disallowed goal, firing a half-volley into the bottom left corner from just inside the area after Wolves twice failed to clear their lines from an initial crossed Everton free kick.
Everton's joy continued right after the restart as they extended their lead just four minutes into the second half when a deep corner was played towards the back post, with Jose Sa failing to make contact with his attempted punched clearance, and the ball bouncing off Craig Dawson's arm and into his own net, leaving Wolves with a mountain to climb.
A flurry of action occurred just after the hour mark when Iliman Ndiaye was denied a fourth for a foul on Sa by Dominic Calvert-Lewin, and moments later, Wolves came within inches of grabbing their first as Jorgen Strand Larsen's header rebounded off the post, though play was called back for a foul on Vitaliy Mykolenko.
The Toffees added a fourth in their demolition of Wolves with 20 minutes left to play, as Dawson's misery was compounded by his second own goal of the evening, this time turning the ball into his own net with a sliding challenge while attempting to intercept Calvert-Lewin's diving header, marking a truly torrid night for the defender.
Dyche's outfit came close to adding a fifth on numerous occasions in the closing stages, but the final whistle eventually called time on a remarkable evening at Goodison Park as they ran out 4-0 victors.
EVERTON VS. WOLVERHAMPTON WANDERERS HIGHLIGHTS
Ashley Young goal vs. Wolverhampton Wanderers (10th min, Everton 1-0 Wolverhampton Wanderers)
Young breaks the deadlock with a superbly taken free kick, Everton have finally scored after four goalless matches!
The 39-year-old steps up to take a free kick from just outside the area and flawlessly bends his effort around the wall into the bottom right corner, a brilliant way to finally secure his 50th Premier League goal.
Sa and Wolves will be deeply disappointed with that goal, as the wall's poor positioning allows the effort to curl around them and find the net.
Orel Mangala goal vs. Wolverhampton Wanderers (33rd min, Everton 2-0 Wolverhampton Wanderers)
Everton do now have their second, there is no taking that one away!
Mangala has well and truly made up for being caught offside in Everton's earlier disallowed goal, smashing in a half-volley from just inside the area after Wolves repeatedly fail to clear their lines from an initial free kick.
Craig Dawson own goal vs. Wolverhampton Wanderers (49th min, Everton 3-0 Wolverhampton Wanderers)
Everton have a third, Dawson hits into his own net!
A deep corner is played towards the back post, with Sa attempting to punch it clear but failing to make contact, and the ball bounces off Dawson's arm and into the back of the net from close range.
Craig Dawson own goal vs. Wolverhampton Wanderers (72nd min, Everton 4-0 Wolverhampton Wanderers)
A night to forget for Dawson, his second own goal of the night!
Everton whip another free kick into the box, which is met by Calvert-Lewin's diving header as he attempts to flick it towards the back post, but Dawson stretches a leg and turns the ball into the bottom right corner, making it four for the hosts.
MAN OF THE MATCH - ASHLEY YOUNG
Young and the Everton defence may have had a difficult season so far, but tonight was a sensational night for them all, particularly Young, who seemed to roll back the years with an outstanding performance.
The 39-year-old netted the opening goal of the match with a stunning free kick, marking his 50th Premier League goal, and was a constant threat with his set-pieces and open play deliveries.
He was also formidable in the defensive areas, making seven tackles, four interceptions, one blocked shot and winning eight duels, an impressive all-round performance.
EVERTON VS. WOLVERHAMPTON WANDERERS MATCH STATS
Possession: Everton 45%-55% Wolverhampton Wanderers
Shots: Everton 13-6 Wolverhampton Wanderers
Shots on target: Everton 4-2 Wolverhampton Wanderers
Corners: Everton 3-4 Wolverhampton Wanderers
Fouls: Everton 10-8 Wolverhampton Wanderers
BEST STATS
WHAT NEXT?
Everton's phenomenal victory ends their recent five-match winless run, and they will now look to build on the result when they host Liverpool in the highly anticipated first Merseyside derby of the season on Saturday.
As for Wolves, their four-game unbeaten streak ends in miserable fashion with a 4-0 defeat, leaving them aiming to bounce back when they face West Ham United in another crucial relegation battle on Monday.
Written by
Ellis Stevens