Bayern started with blistering intensity, creating multiple early chances that forced Matvey Safonov into two crucial saves, but PSG weathered the storm and gradually grew into the game, looking more comfortable in possession and starting to progress further up the pitch on a more consistent basis.
Despite all the quality attacking play from both sides, the opening goal came from a major goalkeeping error, as Safonov's attempted punched clearance from Joshua Kimmich's corner skewed into the six-yard box, where Kim Min-jae quickly reacted to head into the top left corner, handing the hosts a crucial lead just as PSG appeared to have taken control of the game.
Bayern, clearly buoyed by their first-half breakthrough, were back to their assured self in the opening stages of the second 45, and they were handed a further boost when Ousmane Dembele was controversially given a second yellow card for bringing down Alphonso Davies as Bayern broke forward just before the hour mark.
The hosts built pressure following the red card and came excruciatingly close to doubling their lead when Jamal Musiala's curling effort was brilliantly pushed onto the post by Safonov, redeeming himself for his earlier mistake as he kept PSG in with a fighting chance.
Despite PSG remaining in the match as the clock ticked towards the 90th minute, attempting to push forward in search of a late equaliser in the final moments, Vincent Kompany's men held firm to secure the crucial win in Munich.
BAYERN MUNICH VS. PARIS SAINT-GERMAIN HIGHLIGHTS
Kim Min-jae goal vs. Paris Saint-Germain (38th min, Bayern Munich 1-0 Paris Saint-Germain)
Bayern have the lead through Kim, what a soft goal to concede for PSG!
Kimmich gets another chance to deliver the ball into the box after his first corner was cleared by the first man, and his second delivery is much better, curling perfectly on top of the goalkeeper's head.
Safonov attempts to punch the ball clear of his goal, but his connection is poor, diverting the ball into the centre of the six-yard box, where Kim is quickest to react and heads into the top left corner, giving Bayern a crucial lead.
57th min: Ousmane Dembele (Paris Saint-Germain) Red Card
Dembele sees red for a second yellow after a late challenge on Davies, a harsh call by the referee.
Dembele, booked for dissent in the first half, sees his shot blocked by Davies and slides in to challenge as the defender looks to spring Bayern on the break.
The referee initially allows play to continue but pulls it back to show Dembele his second yellow and, consequently, a red card, an extremely controversial decision given the minimal contact by the forward.
MAN OF THE MATCH - JOSHUA KIMMICH
Kimmich was an assured and cultured presence in the midfield throughout the game for Bayern Munich, not only assisting the winning goal with a fabulous corner but also helping the hosts control large portions of the match.
The midfielder registered 81 touches, the third most on the team, and completed 60 passes with 91% accuracy, including one key pass and one big chance created.
Kimmich was also a formidable defender for Bayern, making two tackles, one interception and winning two duels, a truly all-round performance from the German.
BAYERN MUNICH VS. PARIS SAINT-GERMAIN MATCH STATS
Possession: Bayern Munich 57%-43% Paris Saint-Germain
Shots: Bayern Munich 18-11 Paris Saint-Germain
Shots on target: Bayern Munich 7-3 Paris Saint-Germain
Corners: Bayern Munich 4-3 Paris Saint-Germain
Fouls: Bayern Munich 13-10 Paris Saint-Germain
BEST STATS
WHAT NEXT?
Victory for Bayern lifts them to 11th in the league phase table, just a point behind the top eight, and extends their winning streak to seven games across all competitions, a run they will aim to extend when they travel to Signal Iduna Park to face Borussia Dortmund in the Bundesliga on Saturday.
Defeat for PSG sees them worryingly fall out of the qualification places, sitting 25th with just four points from five games, and Luis Enrique will have to first turn his focus to matches against Nantes and Auxerre before attempting to revive their European campaign against RB Salzburg in two weeks' time.