The visitors took just four minutes to break through Les Parisiens, as the ball was turned over to start a swift move that culminated in Luis Diaz squeezing his shot past Marquinhos after Michael Olise’s initial attempt had been saved.
Bradley Barcola then played a wayward pass that resulted in an Aleksandar Pavlovic strike deflecting off Willian Pacho on its way behind.
Despite their struggles, Luis Enrique’s side thought they were back on level terms in the 22nd minute when Ousmane Dembele chested in the ball that Fabian Ruiz had smashed across the box, but he had strayed offside.
There was yet more frustration as Dembele was forced off injured three minutes later, and that feeling only grew when Barcola was released behind Bayern’s backline but couldn’t beat Manuel Neuer.
Gnabry was left in disbelief when his shot hit both posts shortly after, but Diaz soon atoned, as he pickpocketed Marquinhos and fired in off the woodwork.
The hosts just about avoided further punishment after more lax play, as Josip Stanisic saw a goal ruled out for offside and Joshua Kimmich fired narrowly past the post.
Diaz then needlessly tainted the 45 minutes of work that he had been so central to, as the winger was sent off for a poor challenge on Achraf Hakimi that forced the Moroccan to go off injured moments before the break.
Neuer was booked for time wasting within four minutes of the restart as Bayern tried to slow things down, while PSG built up patiently but saw Barcola make a mess of his attempt from Nuno Mendes’ cross.
Vitinha split the visitors’ resolute defence to find Khvicha Kvaratskhelia, but his shot was routinely saved, and the midfielder then saw an ambitious strike of his own palmed away.
Les Parisiens finally got a goal back in the 74th minute, when Joao Neves ghosted into the box to convert from Lee Kang-in’s cross.
The hosts continued to test just how resolute Vincent Kompany’s tiring backline could be, but even when the backline failed, Neuer stood tall to authoritatively deny Warren Zaire-Emery.
Joao Neves and Lee both came agonisingly close to an equaliser, while Jonathan Tah made some vital interventions to help Bayern hold on.
That sees the visitors extend their perfect record in all competitions this term to an astounding 16 matches and take top spot in the UCL table, while also ending PSG’s eight-game unbeaten run.
Flashscore Man of the Match: Jonathan Tah (Bayern Munich)