Gonzalo Higuain and Marek Hamsik put the visitors firmly in control as Rafa Benitez’s side struck twice in the opening 45 minutes before the Slovakian midfielder added a third after the break.
Substitute Manolo Gabbiadini made it four just moments after replacing two-goal hero Hamisk from the bench before former Arsenal striker Nicklas Bendtner pulled a goal back for the hosts.
Wolfsburg came into the clash having lost just once in their last 26 matches in all competitions, a run that included two victories against Italian opposition Inter Milan in the previous round.
And the Germans started the game brightly as they looked to impose their slick passing game on Napoli, but it was the visitors who opened the scoring.
Dries Mertens checked back on to his right foot from wide on the left and delivered an inch-perfect ball over the top for Higuain, who was just onside.
The Argentine striker brought the ball under control with what looked like a combination of chest and upper arm before firing past Diego Benaglio with the outside of his right foot – his seventh of the competition.
The Wolfsburg defenders were rightly aggrieved but their protestations fell on deaf ears as the referee waved away their handball appeals.
They could have no complaints seven minutes later, however, as Hamsik broke clear of the Wolves’ backline to apply a composed finish to a slick, flowing move that ended with Higuain’s defence-splitting pass.
Wolfsburg almost halved the deficit on the stroke of half-time. Former Chelsea forward Andre Schurrle cut in from the left and struck a rasping drive that needed every inch of Mariano Andujar’s frame to tip the effort onto the crossbar.
Some sloppy Wolfsburg play allowed Hamsik to grab his second on 64 minutes as the tie slipped away from Dieter Hecking’s side. Benaglio played the ball out to Josuha Guilavogui, who turned and passed the ball straight to Jose Callejon.
The former Real Madrid midfielder skipped into the penalty are before squaring for Hamsik to turn into an empty net as Napoli took a firm grip on this last eight tie.
It was to be the Napoli captain’s last meaningful contribution as he was replaced by Gabbiadini. The former Sampdoria man made it four just a minute later when he headed Lorenzo Insigne’s perfectly delivered cross past Benaglio.
Wolfsburg had only failed to score in two of their last 26 matches and they had a goal back with 10 minutes left. Ivan Perisic broke to the byline before crossing for Bendtner to tap home.
This was already the Germans’ heaviest home defeat in European competition but it could have been five moments later as Gabbiandini struck the crossbar with a wicked dipping effort from 25 yards.