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The hosts threatened to add a second goal three minutes before the break, with Romelu Lukaku seeing a long-range free kicked palmed away by Benaglio.
They were able to double their lead on the stroke of half time, when Kevin Mirallas saw his effort saved by the keeper and from the rebound Baines unselfishly picked out Seamus Coleman to head in at the back post.
Ivica Olic stung the palms of Howard with a powerful strike, before the keeper was again forced into action to save Gustavo's low attempt.
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Howard continued to frustrate Wolfsburg and the keeper had to be at full stretch to tip Ricardo Rodriguez's free kick wide.
Naldo came within inches of pulling a goal back for the German side with a low free kick that curled narrowly wide of the post.
Everton still looked to pose a threat and they almost scored a fourth on the counter-attack when McGeady curled an effort inches over the top corner.
Nicklas Bendtner was brought on for the visitors and the Danish striker saw a header saved by Howard after connecting with Rodriguez's cross.
Mirallas added a fourth for Everton with a minute left to play as he latched on to a through-ball from Samuel Eto'o, before confidently slotting an effort past the keeper.
In the fourth minute of stoppage time Wolfsburg found the back of the net thorough Rodriguez's curling free kick, but it proved to be little more than a consolation as Everton began their European campaign with a win.