Wolves started brightly but the match turned after the visitors took the lead against the run of play through Jermaine Beckford after 21 minutes.
John Heitinga found Leon Osman in space out on the right and his cross picked out Beckford who got in between Christophe Berra and Richard Stearman to head past Wayne Hennessey.
Phil Neville doubled Everton's lead on 38 minutes. Hennessey managed to keep out at full stretch a misdirected header from 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.
On the stroke of half-time Diniyar Bilyaletdinov made it 3-0 after latching onto a loose pass and breaking from the halfway line to hammer an unstoppable 25-yard shot into the top left corner to clinch the Merseysiders' first win at Molineux since 1982.
