The midfielder scored the game's solitary goal as the Bavarians continued their impressive start to the season despite failing to hit the heights for much of the afternoon.Bayern Munich extended its home winning streak to 12 Bundesliga matches as a Thomas Muller goal gave the club a 1-0 victory against Wolfsburg.
Bayern was far from its best at the Allianz Arena on Saturday, but Muller's 63rd-minute strike was enough, as Pep Guardiola's men kept pace with title rival Borussia Dortmund.
Wolfsburg was resolute throughout, and frustrated its more-fancied opponent in the first half, with Arjen Robben missing Bayern's best chance when he inexplicably poked wide from six yards.
But the home side's quality eventually told, as Muller's smart finish following an excellent Franck Ribery cross saw the club post its 10th win against Wolfsburg in the last 11 attempts.
Both sides rung the changes following DFB-Pokal wins in midweek, with Guardiola making five alterations to his squad as Ribery, Robben and Mario Manduzkic all started while Mario Gotze won a spot on the bench after recovering from his ankle injury.
Wolfsburg made three changes, as attacker Ja-Cheol Koo came in, while former Bayern players Luiz Gustavo and Ivica Olic also started.
Gustavo – who left the Bavarian giant in the close season – almost made his old club pay in the seventh minute as his header forced Bayern goalkeeper Manuel Neuer into a diving save following a Ricardo Rodriguez corner.
Bastian Schweinsteiger then had a headed effort at the other end, but early chances were limited as Wolfsburg sat back and soaked up the pressure.
The club did a good job of frustrating Bayern, and goalkeeper Diego Benaglio did what he needed to keep out Muller's drive from an acute angle, before Robben inexplicably poked wide from six yards just before the break.
Robben went down twice in the early stages of the second half as he looked for a penalty, while Muller - who was consistently finding space - was denied by the onrushing Benaglio.
And at the other end, Marcel Schafer wasted a golden chance, unable to direct his diving header on target following an excellent Christian Trasch cross.
That chance served a warning to Bayern, and Guardiola quickly introduced Xherdan Shaqiri and Toni Kroos for Robben and Schweinsteiger in a bid to change things, but it was two of his other stars that finally gave the European champion the lead.
Ribery broke down the left and played a superb ball across the face of goal, and although Mandzukic was unable to meet it, Muller powered home a far-post finish from a tight angle.
Bayern almost scored a second, but Mandzukic saw his effort cleared off the line by Naldo, while the Brazilian defender forced Neuer into a smart save at the other end with a powerful header.
But Bayern did just enough for victory as Wolfsburg lost its fourth away match in as many outings this term.