Meanwhile, Borussia Dortmund’s away woes continued as they fell to a 3-1 defeat against Mainz, with Emre Can’s first-half red card adding to their troubles.
In a tense clash at the Millerntor-Stadion, Bayern came up against a St. Pauli side eager to score their first home goal of the season.
The former German champions controlled possession from the outset but found it difficult to break down St. Pauli’s disciplined defence.
The breakthrough finally came in the 22nd minute when Musiala, picking up the ball 35 yards out, unleashed a stunning shot that soared past goalkeeper Nikola Vasilj, clipping the crossbar on its way in.
Despite Bayern’s best efforts, St. Pauli’s compact setup prevented further goals, though the hosts failed to muster a shot on target.
Over in Mainz, Borussia Dortmund’s away form continued to disappoint as they suffered a 3-1 loss.
Dortmund started brightly, pressing high and controlling early possession, but a reckless challenge by Emre Can in the 27th minute saw him sent off, tilting the game in Mainz’s favour.
Shortly after, Jae-sung Lee capitalised on Dortmund’s defensive lapse, heading in the opener.
Although Serhou Guirassy equalised from the penalty spot after Lee’s foul, Mainz swiftly regained the lead through Jonathan Burkardt just before halftime.
In the second half, a deflected shot from Paul Nebel sealed Dortmund’s fate, handing them their sixth straight away defeat across all competitions.
The loss adds pressure on Dortmund manager Nuri Sahin, whose team has failed to register an away win in the Bundesliga this season.
At the Vonovia Ruhrstadion, Bayer Leverkusen lost further ground on league leaders Bayern as they were held to a 1-1 draw by struggling VfL Bochum.
Patrik Schick gave the reigning champions a first lead but Koji Miyosh netted a late equaliser to earn a share of the spoils for the bottom-of-the-league club.
Elsewhere, a late goal from substitute Oliver Burke powered high-flying Werder Bremen to a fine 2-1 victory over Holstein Kiel.