Three eye-catching goals in a sparkling spell before half-time enabled depleted Everton to overpower relegation-threatened Wolves at sunny Molineux.
The hosts started well, but Jermaine Beckford nicked a 21st-minute lead by glancing in Leon Osman's wicked cross.
Phil Neville then rifled into the top corner after Wolves goalkeeper Wayne Henessey prevented a comical own goal.
Diniyar Bilyaletdinov soon cracked home a stunning 25-yard drive before half-time as Everton took complete control.
David Moyes' Europa League-chasing team moved a point behind sixth-placed Liverpool with a deserved win, but the three points looked far from their reach during a backs-to-the-wall start in which they were forced to prove their evergreen defensive qualities.
Wolves, who had been relatively prolific in recent home games, began with a high tempo against an Everton team for whom 22-year-old Victor Anichibe was the oldest outfield substitute.
Making his first appearance since suffering a leg-break in September, Adlene Guedioura had a decent early shot blocked by determined Neville after the Algerian midfielder had eluded Everton debutant Magaye Gueye on the edge of the box with perceptive chest control.
Home striker Steven Fletcher then punched a strong header towards goal from a dangerous corner soon after but, with Tim Howard well beaten, it was headed off the line by an alert Osman.
Everton rarely got out of their own half in the opening 20 minutes as Wolves pressed with intent while dominating possession.
The Molineux faithful leapt from their seats when Sylvan Ebanks-Blake went down under pressure from Phil Jagielka in the area, but referee Phil Dowd ruled that it was an innocuous tussle.
And that marked moment the tide turned in spectacular fashion.
Producing a classic counter-punch in the 20th minute, Osman cleverly drifted behind his marker out wide to deliver a cross which Beckford – who gambled into space at the front post – clinically glanced high into the net with Hennessey in no position to make a save. The former Leeds United striker's fourth goal in his last seven Premier League appearances completely drained the confidence out of a Wolves side who had failed to make their explosive start count.
Guedioura – who looked brimming with promise on his return – curled a shot just wide of Howard's upright soon after, but any collective conviction from the hosts disappeared. Lax George Elokobi tackling again allowed Osman to break free, once again, down the right wing after half-an-hour.
He unleashed another superb cross for Beckford but, completely unmarked, his powerful downward header was athletically palmed away by the increasingly-overworked Hennessey.
Seconds later a superb point-blank block from Phil Jagielka stopped Sylvan Ebanks-Blake stroking the ball in from six yards.
From Osman's inswinging corner Elokobi looked to have scored a spectacular own goal as the ball flew off his back, but Hennessey amazingly clawed the ball away.
Yet Beckford immediately recycled the ball by teeing it up for Neville, who hammered the short pass back past unsighted Hennessey from the right-hand corner of the penalty area without a second thought.
The visitors should have added a third straight after but onrushing French youngster Gueye, who was clean through, poked his weak left-foot effort at an outstretched Hennessey.
With half-time close, Wolves shot themselves in the foot when Jamie O'Hara let the ball run loose as confusion reigned amongst their midfield. Russian midfielder Bilyaletdinov wasted no time in making a direct route for goal before unleashing a devastating long-range drive into the roof of Hennessey's goal.
With the contest effectively over the second half was a more muted affair, though Everton did have to stand strong when questions were asked of them. The hosts appealed for a penalty when a shot from Matt Jarvis, who did not wilt despite having a difficult time creating clear openings, came back off Tony Hibbert's arm inside the area.
Once again referee Dowd, who had a clear view of the incident, waved their appeals away.\
Howard came to Everton's rescue as they briefly nodded off with the match drifting, saving smartly from Karl Henry's powerful 65th-minute shot before Guedioura's strong header tested the American goalkeeper's most basic instincts to the full.
With 10 minutes left, Bilyaletdinov missed a simple chance to add a gloss to the scoreline.
By Chris Wyatt, BBC Sport
Everton take their quest for an unlikely European berth to the Black Country this weekend for an early Saturday afternoon clash with Wolves. With an injury list almost as long as that of the players who have been farmed out on loan, David Moyes will have few options when he selects his starting XI for a fixture that has ended all square in each of the last three occasions.
The manager will be buouyed, however, by the performance of Magaye Gueye against Aston Villa last Saturday when he came on to replace the injured Seamus Coleman and made the most of his first Premier League appearance since joining the Blues last summer.
The Frenchman may get the nod in a starting role if Coleman isn't passed fit when he undergoes a late test. Tim Cahill and Jack Rodwell will also be assessed for their ability to play after missing the last few games with foot and ankle injuries respectively.
With all but one of his senior strikers sidelined or on loan, Moyes will once again rely on Jermaine Beckford who is without a goal now in five games but Apostolos Vellios showed some nice touches himself as a late sub in the 2-2 draw with Villa and that, coupled with his form for the Reserves, may earn him another run-out at some stage.
Everton's biggest challenge will be breaking down a Wolves defence that frustrated them in the reverse fixture back in August. Leon Osman's comments in the lead up to the game suggest that the Blues are aware of teams' propensity to sit back and challenge them to break them down, knowing that Moyes's players have struggled to score enough goals this season.
Compounding that will be Wolves' own form on their home ground in recent weeks. They've lost only one of their last five at Molineux including victories over Manchester United and Chelsea, a 3-3 draw with Spurs, and a 4-0 drubbing of Blackpool. Clearly Mick McCarthy has his players fearing no-one on home turf.
Nevertheless, the Midlanders are a place off the bottom and fighting for their top-flight survival once more so while it should be a difficult game for Everton, it's one they can win if they go about it the right way.
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* Everton deducted 10 points for PSR breachView full table