A 15th minute own goal from Ricardo Rodriguez got the hosts off to a bright start and Seamus Coleman added a second just before the break with a stooping header at the back-post.
Leighton Baines converted a penalty within less than a minute of the second half getting underway, while Kevin Mirallas made it four late on after racing through on goal to beat Diego Benaglio.
The visitors had threatened in the second period – forcing Tim Howard into a number of fine saves – and Rodriguez pulled one back in stoppage time with an inch-perfect free-kick.
“It was a really good evening,” said Martinez. “I thought we did a lot of talking about European nights at Goodison and it was phenomenal to see the fans and it was pleasing to finish with that scoreline.
“It’s fair to say Wolfsburg have energy so we stopped their pressure and if you stop that you stop them being a real threat.
“We tried to play through them and use the gaps. We used our pressure better than them and got some opportunities by being well organised.
“It was a really open game between teams who wanted to get on the ball and the fans enjoy watching us play.”