Bundesliga: Bayern Munich 1 Wolfsburg 0
Bayern were far from their best at the Allianz Arena on Saturday, but Muller's 63rd-minute strike was enough, as Pep Guardiola's men kept pace with title rivals Borussia Dortmund.
Wolfsburg were resolute throughout, and frustrated their more-fancied opponents in the first half, with Arjen Robben missing Bayern's best chance when he inexplicably poked wide from six yards.
But the hosts' quality eventually told, as Muller's smart finish following an excellent Franck Ribery cross saw them post their 10th win against Wolfsburg in their 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 giants 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 of the hosts.
They 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 champions 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 their fourth away match in as many outings this term.