Croatia forward Mandzukic scored twice against his former team to take his tally to five after Bastian Schweinsteiger had given the hosts a 24th-minute lead in an impressive display of attacking football by the Bavarians, who have 15 points.
Second-placed Eintracht Frankfurt came back twice, including from two goals down, to earn a 3-3 draw at home to champions Borussia Dortmund, who dropped to fifth place on eight points.
Schalke 04 beat Mainz 05 3-0, with Jefferson Farfan scoring from the spot in the first half and Lewis Holtby and Teemu Pukki striking late, as they moved up to third spot on ten points. Bayern, who have won all their matches domestically and in Europe so far this season, made their intentions known from the start and Schweinsteiger twice rattled the woodwork in the opening 18 minutes as they poured forward.
The Germany midfielder did even better six minutes later when Franck Ribery, who had just driven a low shot narrowly wide, chased the ball down and cut it back into the box for Schweinsteiger who volleyed home to give Bayern a deserved lead. New signing Mandzukic, sparkling in the absence of the injured Mario Gomez, twice came agonisingly close and Arjen Robben saw his 14-metre drive palmed away by goalkeeper Diego Benaglio as the hosts attacked at will.
“Although we dominated throughout, Wolfsburg were not an easy opponent,” Bayern coach Jupp Heynckes told reporters. “We failed to add another after our 1-0 lead despite the number of good chances. It was only settled after we scored to go 2-0 up.”
Mandzukic made amends for his earlier misses when in the 57th he headed in a pinpoint Xherdan Shaqiri cross. Wolfsburg’s Ricardo Rodriguez almost snatched a surprise equaliser against the run of play but his powerful shot from a tight angle scraped the post from their only real chance. Mandzukic struck again to put the outcome beyond doubt, connecting with a Philipp Lahm cross from the right in the 65th to dash any hopes of a Wolfsburg comeback.