The Bavarians, missing half a dozen players through injury, only briefly hit top form in the first half but it was enough to see them notch their first three points of the season.
With Germany coach Joachim Loew in the stands, Mueller flicked in a Robben cutback in the 37th minute after the winger spectacularly shook off two defenders.
Robben then added a goal himself two minutes after the restart with Croatian Ivica Olic cutting the deficit in the 52nd for the visitors as the German league season got underway.
"For every coach in the world victory is the most important thing," Bayern coach Pep Guardiola told reporters. "After our 2-0 lead we did not control the game and we had power only for 65-70 minutes. We still need some time."
Guardiola stuck to his new-look three-man defence despite the absences and with defender Holger Badstuber making his league comeback after two cruciate ligament tears and an injury break of 20 months.
"We did it well today despite not having played with such a team before," former Germany international Badstuber told reporters. "In the second half we ran a bit out of steam but overall it was a very good start."
The hosts were missing among others Franck Ribery, Bastian Schweinsteiger and Thiago Alcantara, so 17-year-old Gianluca Gaudino, the son of former Germany international Maurizio Gaudino, and new signing Juan Bernat got the chance to shine.
With Bayern pressing high up the pitch, Wolfsburg had trouble carrying the ball forward and after 20 minutes Bayern increased the tempo, twice coming close to scoring through Poland forward Robert Lewandowski.
Last season's Bundesliga top scorer, who joined from Bayern's rivals Borussia Dortmund in the close season, was denied by substitute goalkeeper Max Gruen on both occasions before Mueller tapped in to give the hosts the lead.
It only took two minutes of the second half for Bayern to add another goal, with Robben stealing the ball from France international Josuha Guilavogui in midfield and completing the swift move himself after a one-two with Lewandowski.
However, former Bayern forward Olic then silenced the 71,000 crowd with a stunning left-foot shot from 18 metres to give the 2009 champions fresh hope.
Junior Malanda should have grabbed the equaliser 10 minutes from time when he raced into the box but saw his first effort deflected by keeper Manuel Neuer on to the bar before the ball then bounced off the Belgian's foot and rolled wide.
"We played well for 30 minutes and then Bayern increased the pace but we still had the chances to come back," said Wolfsburg coach Dieter Hecking. "We lost possession a bit too easily sometimes and that is something that makes me angry."
Last season's runners-up Dortmund host Bayer Leverkusen on Saturday.