Musiala shines as 10-man Bayern go top despite Neuer row
The win, Bayern's first league victory in 2023, was marred by a late VAR decision to chalk off a Wolfsburg goal, which would have made the score 4-3 with seven minutes plus stoppage time remaining.
Bayern went into the game just hours after sporting director Hasan Salihamidzic said he was "disappointed" with injured captain Manuel Neuer for putting "his personal interests above" the club.
Neuer, who is currently out injured with a broken leg from a skiing accident in December, criticised the club's decision to fire long-time goalkeeping coach Toni Tapalovic, saying he felt "as if my heart had been ripped out".
Speaking with German tabloid Bild, Salihamidzic said: "I understand Manuel is affected personally, but as captain I would have expected a different attitude from him."
On the pitch, Bayern played the majority of the second half on Sunday with 10 men after midfielder Joshua Kimmich picked up a second yellow card.
Bayern struck in the ninth minute through France forward Kingsley Coman, whose curling cross evaded a leaping Thomas Mueller but drifted past goalkeeper Koen Casteels and into the net.
Coman added another just five minutes later, hammering a floating Joao Cancelo ball past a helpless Casteels.
Coman then won a free-kick just outside the Wolfsburg box and Mueller headed in Kimmich's delivery to make it 3-0 with less than 20 minutes gone.
The goal, Mueller's first since September, came on his 427th league appearance for Bayern, equalling Gerd Mueller's all-time record.
Wolfsburg manager Niko Kovac, who won the league and cup double in charge of Bayern, took off centre-back Maxence Lacroix for winger Jakub Kaminski after just 30 minutes.
The change had an almost immediate impact, with the Polish international scoring late in the first half to give the home side hope.
Kimmich picked up a second yellow for a foul on Wolfsburg's Max Arnold 10 minutes into the second half, prompting Julian Nagelsmann to make three changes.
Wolfsburg went on the attack immediately and should have had a second when Kaminski found an unmarked Ridle Baku in the box, but the midfielder headed the ball directly at Bayern 'keeper Yann Sommer.
Despite their numerical disadvantage, Bayern absorbed waves of Wolfsburg pressure and were next to get on the scoresheet thanks to a sensational goal from Musiala.
Musiala collected the ball near the sideline and dribbled through the heart of the Wolfsburg defence, slaloming past several defenders before unleashing a low shot to beat Casteels.
Wolfsburg scored a second with 10 minutes remaining through Mattias Svanberg.
The 2009 Bundesliga winners had the ball in the net against just two minutes later, but the goal was controversially disallowed for a foul in the build-up.
The win saw Bayern reclaim their one point lead over second-placed Union Berlin.
Wolfsburg, who had won six in a row to sit on the edge of the European placings, have now lost their past three matches in all competitions.
Bremen sink Stuttgart
Goals from Jens Stage and Marvin Ducksch carried Werder Bremen to a 2-0 away win that left Stuttgart in the relegation play-off spot.
Bremen's Niclas Fuellkrug, the league's leading scorer this season with 13 goals, had a first-half effort ruled out for a limp push in the back of Stuttgart defender Hiroki Ito.
The Germany striker broke through on the counter in the 59th minute, losing possession when about to strike, but the ball bounced into the path of Danish midfielder Stage, who hammered into the roof of the net.
The goal rattled Stuttgart and with Bremen turning up the pressure, Ducksch added a second.
The win, Bremen's second in a row, sent the promoted side up to eighth, just two spots from the European placings.