The hosts took the lead on 15 minutes courtesy of helpless Wolfsburg defender Ricardo Rodriguez as Steven Naismith’s strike cannoned off him via goalkeeper Diego Benaglio, before Seamus Coleman added a second on the stroke of half-time with a close-range header.
Leighton Baines then made it three from the penalty spot within less than a minute of the restart after Aiden McGeady was brought down, while the inspired Tim Howard was called into action with a number of smart second-half saves.
Kevin Mirallas added a fourth in the dying stages as he raced onto a through ball from substitute Samuel Eto’o to slot beyond the onrushing Benaglio with a composed finish, before Rodriguez pulled one back at the right end in stoppage time with a fine free-kick.
Wolfsburg only missed out on qualifying for the Champions League by a point and they dominated the opening 10 minutes.
But it was Everton who opened the scoring when a lovely move ended in the unfortunate Rodriguez being credited with an own goal.
Naismith began things with a neat turn in midfield before finding James McCarthy, who played the ball into the penalty area for the onrushing Baines.
The full-back squared it to Naismith, whose shot was met with an attempted clearance from Rodriguez that hit Benaglio and then bounced back off the left back before rolling into the net.
Wolfsburg reacted well and Howard had to be alert to save a well-struck shot from the dangerous Luiz Gustavo.
There were openings at both ends and more good play from in-form Naismith allowed Romelu Lukaku his first sight of goal.
Unfortunately for the Belgian, who was coveted by Wolfsburg before joining the Toffees permanently in the summer, he slipped just as he shot and managed to block his own effort.
McGeady then saw his shot blocked by the legs of Naldo, while Wolfsburg were not quite managing to find the mark with their crosses and long-range efforts.
Lukaku was proving hard to handle for the Wolfsburg defence and he tested Benaglio with a 30-yard free-kick after being caught by Junior Malanda.
With the board showing two minutes of stoppage time having just gone up, Everton doubled their lead.
Benaglio again played an unwanted role, this time flapping at a Mirallas shot, which was seized on by Baines.
The full-back may have intended to shoot but his side-footed effort turned into a perfect pass for Coleman to head into an empty net.
And things got even better for Everton immediately after the break when a wayward pass across the danger area from Maximilian Arnold played in McGeady, who was brought down by Robin Knoche.
Contact was outside the box but referee Luca Banti awarded the penalty and Baines found the bottom corner.
That was surely that as far as Wolfsburg were concerned but the lively Rodriguez finished off a decent move by testing Howard with a shot from a tight angle on the left before Arnold shot just past the post.
It was Wolfsburg’s best spell of the game, and moments later Daniel Caligiuri brought another save out of Howard, who was grateful to see Gustavo place a follow-up shot into his arms.
Rodriguez’s left foot was certainly a danger to Everton and his 25-yard free-kick had Howard flying across goal to push the ball away.
With half an hour remaining, Wolfsburg boss Dieter Hecking sent on former Arsenal striker Nicklas Bendtner, who was greeted by a smattering of boos from the Everton fans.
Wolfsburg continued to test Howard with Kevin De Bruyne forcing the best save of the night with a curling effort.
Naismith received a standing ovation when he left the field (81) and was replaced by Darron Gibson, making his first Everton appearance in almost a year.
Gibson was denied a dream comeback when Benaglio saved his shot but Everton did manage a fourth in the 89th minute, substitute Eto’o playing in Mirallas, who calmly found the bottom corner.
The scoreline ultimately flattered Everton, and it was probably little consolation to Wolfsburg that they found the net late on, with Rodriguez firing in off the post from 25 yards with the final kick of the game.