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 10 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.
MANY CHANCES
"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.
Dortmund, struggling to find consistency this term, failed to bounce back from Saturday's 3-2 loss at Hamburg, squandering a two-goal first half lead as Frankfurt scored in the 49th and 51st minute with Stefan Aigner and Japanese Takashi Inui.
Substitute Mario Goetze put them back in front three minutes later from close range but surprise package Frankfurt, who won their first four games, rallied again through Bamba Anderson's header midway through the second half to rescue a point.
"That was the best performance I have seen from a Frankfurt team," said Dortmund coach Jurgen Klopp. "They have had many good teams in the past but this was top quality."
Promoted Fortuna Dusseldorf continued their fine start with a 2-0 win at Greuther Fuerth to go fourth on nine points.
‘Managing Leeds? It was an option that appeared, but it wasn’t the right timing. I decided it wasn’t a good idea to leave the club I was at mid-season’: Premier League boss admits to turning down opportunity to replace Jesse Marsch in 2023
‘Ruben Amorim could have waited for Real Madrid and had a better chance to be successful – to have joined Manchester United, he must be convinced in his own ability’ Former Old Trafford coach’s verdict on new boss
