The Toffees, back in the tournament for the first time since 2010, controlled much of the game as a Ricardo Rodriguez own goal and a Seamus Coleman header gave them a 2-0 half-time lead.
Leighton Baines put the game beyond Wolfsburg with a second-half penalty.
Kevin Mirallas drilled in a late fourth for Everton before Rodriguez grabbed a consolation with a curled free-kick.
The win puts Everton top of Group H and was just reward for manager Roberto Martinez, who underlined his intention to take the competition seriously by naming a strong side, after calling it "the perfect next step" for the club.
The Toffees narrowly missed out on the Champions League last season as they finished fifth in the Premier League, but with their participation in this season's Europa League ending a four-year absence, Martinez has expressed a determination to go as far as possible.
Everton's attacking display on Thursday will certainly give him confidence of progressing from a group that also contains French side Lille and Russians FK Krasnodar.
Martinez had opted not to rest any of his first-team regulars for the visit of Wolfsburg, naming the same side that defeated West Brom 2-0 in the Premier League on Saturday.
Romelu Lukaku got his first of the campaign in that game and the striker spearheaded an exciting, attacking quartet that also included Aiden McGeady, Naismith and Mirallas.
They have all contributed to Everton's impressive statistic of having scored at least two goals in every game this season, and it was of little surprise they each played significant roles in the goals against Wolfsburg.
Naismith was the first to make a telling contribution, forcing the opener with Everton's first attack. After winning possession, Naismith ran into the area to receive a Baines pass before stabbing a shot at goal. Rodriguez tried to clear, but the ball cannoned off goalkeeper Diego Benaglio, and hit the Wolfsburg full-back again before ending up in his own net.
That was Everton's first goal in Europe at Goodison Park since beating Sporting Lisbon 2-1 in February 2010, and it had the buoyant home crowd hungry for more.
Everton duly attempted to deliver, with full-backs Baines and Coleman becoming more adventurous as Wolfsburg offered little going forward, and their attacking instincts resulted in the home side's second goal on the stroke of half-time.
Mirallas's drive was weakly pushed into the path of Baines, who had followed the shot into the area, and he knocked the ball across goal for Coleman to nod in.
Wolfsburg boss Dieter Hecking introduced Germany midfielder Aaron Hunt for the start of the second half, but within seconds of the restart Everton went further ahead. This time, Robin Knoche's foul on McGeady was deemed to have occurred inside the area, and Baines confidently despatched the resulting penalty.
The goal effectively ended Wolfsburg's hopes of returning to Germany with anything to show but, with nothing to lose, they embarked on a spell of dominance.
For a good 30 minutes they enjoyed the lion's share of possession and attempts on goal, as Tim Howard produced saves from Luiz Gustavo's opportunistic shot and Rodriguez's well-struck free-kick.
Former Arsenal striker Nicklas Bendtner was introduced after the hour, with Wolfsburg boss Hecking sensing a possible goal, but instead it was Everton who grabbed a fourth. Mirallas peeled away from defenders to run on to substitute Samuel Eto'o's through ball and he coolly slotted in at Benaglio's near post.
There was still time for Wolfsburg to get the consolation their 27 shots on goal deserved, Rodriguez making some amends for his early own goal with a curling free-kick.
Everton boss Roberto Martinez: "The atmosphere was perfect for us to start a very good performance.
"I thought there were two very good sides. On the night the scoreline probably doesn't reflect the difference between the two sides.
"We scored at the right times. Our work-rate was magnificent. We had to defend and we did that really well but every time we went forward we had a clinical touch about us."
Wolfsburg boss Dieter Hecking: "It's obviously not the start we'd hoped for. We were lacking in certain areas, both in terms of finishing and defensive work.
"We should have gone into half-time a goal down and we got hit with a second just before the break. Straight after the restart, 3-0 down and the game is lost.
"We really weren't smart enough and showed a certain naivety."
Everton marked their Europa League return with a dominant victory over Germans Wolfsburg at Goodison Park.