Wolves dominated proceedings in the opening 20 minutes in the West Midlands but Jermaine Beckford headed in a Leon Osman cross in the 21st minute to put the visitors ahead.
Phil Neville then added a superb second from the edge of the box in the 39th minute before Diniyar Bilyaletdinov scored an equally impressive third on the stroke of half-time.
Wolves did create chances to reduce the deficit after the interval but Everton were equally as dangerous going forward and could easily have added to their tally.
Still, the three points move them to within a point of Liverpool ahead of their game against Manchester City on Monday night, whereas Wolves are now facing a huge fight to remain in the division after a second successive defeat.
The loss of key striker Kevin Doyle through knee ligament damage has had a massive impact on the make-up of the side as he was the ideal player to operate in a 4-5-1 formation.
With Mick McCarthy starting with two upfront, Wolves found themselves exposed in midfield without the extra man and their defending also left a lot to be desired.
They started purposely, however, and Adlene Guedioura had a shot blocked by Neville on the edge of the box at the expense of a corner.
Osman then came to Everton's rescue by clearing Steven Fletcher's header off the line from a Matt Jarvis flag-kick after seven minutes so it was against the run of play when Beckford put Everton ahead after 21 minutes.
John Heitinga found Osman in space out on the right and his cross picked out Beckford, who got in between Christophe Berra and Richard Stearman and in front of Wayne Hennessey to nod home.
Wolves tried to respond instantly and Guedioura was only just off target with a curling attempt from 20 yards out.
However, Beckford came close to doubling Everton's lead after 31 minutes when he got on the end of another Osman cross with a downward header which Hennessey did well to parry away.
A dipping attempt from Jamie O'Hara was deflected just wide and Sylvan Ebanks-Blake had a shot blocked from close range from a Jarvis centre as Wolves again sought a way back but Neville doubled Everton's lead after 38 minutes.
Hennessey, at full stretch, managed to prevent an own goal by George Elokobi from Leighton Baines' corner but the ball landed at the feet of Neville on the edge of the Wolves box and his rising shot flew past Hennessey into the roof of the net.
Then, on the stroke of half-time, Bilyaletdinov made it 3-0 when Wolves lost the ball just inside their own half and allowed the midfielder to progress forward before firing past the despairing dive of Hennessey from 25 yards.
McCarthy made a half-time substitution with Michael Kightly replacing Ebanks-Blake, who had sustained a hamstring injury.
Bilyaletdinov became the first player to be yellow-carded after 51 minutes for bringing down Guedioura before Karl Henry almost gave the home fans something to cheer about at last as his powerful drive was turned aside by Tim Howard.
The Everton keeper then parried a Guedioura header from a Jarvis centre.
Berra blocked an effort from Osman as the Toffees went in search of a fourth late on, while substitute Victor Anichebe had a shot deflected just wide of the post with Hennessey wrong-footed.
Bilyaletdinov definitely should have made it 4-0 but shot over from close range after Elokobi mis-kicked.