Ricardo Rodriguez inadvertently diverted the ball into his own net after a quarter of an hour, before Seamus Coleman doubled the Toffees' lead on the stroke of half-time. A Leighton Baines penalty increased the deficit shortly after the restart and Kevin Mirallas made it 4-0 with a minute left, before Rodriguez fired home a late consolation from a free-kick.
It was a miserable night from start to finish for the Wolves, but there was more than an element of misfortune about Everton's opening goal after 15 minutes. Rodriguez managed to block Steven Naismith's goal-bound effort, but the Swiss international's clearance cannoned off goalkeeper Diego Benaglio and back onto Rodriguez before trickling into the unguarded net.
Benaglio pulled off a fine save to deny former Chelsea FC striker Romelu Lukaku two minutes before the break, but the keeper was unable to prevent Seamus Coleman doubling the hosts' advantage after failing to palm Kevin Mirallas' powerful effort out of harm's way.
Things went from bad to worse for Wolfsburg shortly after the break. Robin Knoche was adjudged to have fouled Aiden McGeady inside the penalty area, prompting the referee to point to the spot. Up stepped Baines, who sent Benaglio the wrong way to rub salt into the Wolves' gaping wounds.
Rodriguez tested Tim Howard with a swerving free-kick and substitute Nicklas Bendtner headed into the American's hands from close range, but the Lower Saxony outfit fell further behind when Mirallas slotted home with a minute left. Rodriguez then curled a superb free-kick in off the post in stoppage time, but it was little more than a consolation for the Wolves.
Everton: Howard - Coleman (Osman 90'), Stones, Jagielka, Baines - Barry, J. McCarthy - McGeady, S. Naismith (Gibson 82'), Mirallas - Lukaku (Eto'o 69')
Wolfsburg: Benaglio - S. Jung, Naldo, Knoche, Rodriguez - Junior Malanda (Hunt 46'), Luiz Gustavo (Guilavogui 77') - D. Caligiuri (Bendtner 61'), Arnold, De Bruyne - Olic
Goals: 1-0 Rodriguez OG (15'), 2-0 Coleman (45'), 3-0 Baines pen (47'), 4-0 Mirallas (90'), 4-1 Rodriguez (90')