Dieter Hecking's side held a 3-2 lead over the Belgians, who are also in their first knockout campaign of Europe's elite competition, and managed to come away with a 4-2 aggregate win in the Round of 16 thanks to Andre Schurrle's second-half goal.
Die Wolfe managed to get a footing in the contest with Max Kruse, Josuha Guilavogui and Schurrle all going close before taking up the running early in the second half with some confident play that had the visitors frustrated.
In the 74th minute, Wolfsburg eased any tension when Julian Draxler received the ball wide out on the right before advancing powerfully to the byline before cutting back for Schurrle to finish neatly with a low shot from just outside the six-yard box.
The Bundesliga club will now move through to the final eight of the top league in Europe in what has already been a savagely successful campaign for the team that sits seventh in their domestic league.
2015/16 UEFA Champions League - Round of 16 second leg