Dani Alves, Edinson Cavani and Neymar found the net, with Kylian Mbappe also making his mark with two assists, to put PSG top of Group B with a maximum six points.
Bayern, who started with defender Mats Hummels and wingers Arjen Robben and Franck Ribery on the bench, lacked pace up front and were overwhelmed at the back despite a good spell in the middle of the first half.
The German champions are level on three points with Celtic, who beat pointless Anderlecht 3-0 away.
Lukaku double leads Man United to 4-1 win
Romelu Lukaku struck twice to lead Manchester United to an emphatic 4-0 away win over CSKA Moscow in Group A yesterday.
The Belgian striker headed home after four minutes and tapped in just before the interval for his 10th goal of the season to put the English Premier League side 3-0 ahead at halftime.
Anthony Martial had slotted home a penalty in between and Henrikh Mkhitaryan added a fourth in the second half to give United a maximum six points from their opening two matches.
Konstantin Kuchaev grabbed a late consolation for CSKA.
United, without first-choice central midfielders Paul Pogba, Marouane Fellaini and Michael Carrick, lead the group by three points from CSKA and Basel.
Higuain on target as Juve win
Gonzalo Higuain came off the bench to open the scoring for Juventus and Mario Mandzukic added a second as the Italian champions beat Olympiakos 2-0 in their Group D clash.
With Juve dominating possession but failing to create many goal-scoring opportunities, Argentine striker Higuain entered the fray on the hour mark and fired home the rebound from his own shot nine minutes later to give Juve the lead.
With Olympiakos seeking to score on the counter, Juventus spent much of the game bombarding the Greek side’s penalty area with crosses, free kicks and corners and Mandzukic went close with a trio of headers before finally bundling the ball home in the 80th minute.
Having lost their opening game 3-0 to Barcelona, the win puts Juventus back on track and in third place in Group D on three points behind Sporting of Portugal on goal difference, while two defeats in their opening two games leave Olympiakos bottom.