The French team tore the German visitors' defense apart on the counterattack and took command of Group B with goals from Dani Alves, Edinson Cavani and Neymar.
Kylian Mbappe, who was hired alongside Neymar this summer for a combined 400 million euros ($470 million), did not score but tormented the Bayern defense throughout with his dribbling ability and frenetic pace. He was decisive in setting up Neymar's goal.
After scoring eight goals without conceding in their first two matches, PSG leads the group with six points, with Bayern and Celtic tied for second place with three points. Celtic won 3-0 at Anderlecht in the group's other match yesterday.
Bayern coach Carlo Ancelotti unexpectedly left wingers Arjen Robben and Franck Ribery on the bench, opting for a more defensive approach with Arturo Vidal and Corentin Tolisso instead.
Ancelotti also gave starting roles to Niklas Sule and Javi Martinez in the heart of his defense, at the expense of Mats Hummels and Jerome Boateng, with the latter being left out of the squad.
There was no surprise in Unai Emery's line-up, with the attacking trident of Neymar, Mbappe and Cavani starting at the Parc des Princes in a 4-3-3 formation.
Neymar cut inside through a sea of legs and delivered a perfect assist on the right of the box for the unmarked Dani Alves, who fired home from a tight angle just two minutes into the match.
Bayern did not panic and tried to regain composure with a spell of possession. It worked, and Javi Martinez came close with a shot from the edge of the box that forced 'keeper Alphonse Areola to palm the ball over with a diving save.
PSG did not take advantage of its chances, though, until Cavani made it 2-0 near the half-hour mark, curling a beautiful shot in the top corner from Mbappe's assist to beat 'keeper Sven Ulreich.
Ancelotti brought on former PSG academy graduate Kingsley Coman and Sebastian Rudy after the interval to turn things around. The pair added an extra dose of danger as Bayern looked more incisive, but the visitors continued to be vulnerable to counterattacks as Mbappe and Neymar combined on the edge of the box, only for the Brazil star to send his shot wide.
Bayern could not even get a consolation goal as Robert Lewandowski hit the woodwork in added time.
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