It was plain sailing for Unai Emery's men, who extended their unbeaten run at the Parc des Princes to 37 matches in all competitions, taking them three points ahead of their opponents in what is expected to be a two-way battle for top spot.
PSG were ahead with less than 90 seconds played thanks to an Alves strike, coming at the end of a skillful run from Neymar that took a number of Bayern players out of the equation.
Alves was left with the task of belting past Sven Ulreich from close range, which he managed to do so despite a heavy first touch which allowed the stand-in Bayern stopper to narrow the angle.
The visitors were creating more chances than their opponents, one of which fell the way of Thomas Muller 12 minutes in as he failed to turn a right-sided cross on target.
Breaking forward in numbers was proving to be a smart tactic for the French outfit, particularly paying off 32 minutes in when Kylian Mbappe burst into the box and held the ball up for Cavani, who in turn sent the ball flying past Ulreich from right on the edge of the area.
Cavani really should have killed the game off before the interval, only to see his one-on-one attempt kept out by Ulreich as Bayern again fell apart at the back in the absence of Jerome Boateng and Mats Hummels.
Much like in the first half, Bayern were seeing plenty of the ball and creating some good openings, and they so nearly had a route back into the match as Martinez saw his shot blocked on the line by Thiago Silva.
Rudy and Niklas Sule also saw chances come and go, before Neymar put the game to bed by helping Mbappe's cross over the line after Bayern struggled to stop the France international's run.
Bayern, victorious on each of their last three visits to this country, were denied a goal moments later when Arturo Vidal's close-range finish was ruled out for offside.
Alves blasted wide from a good position and Coman tested Areola at the other end as the match petered to its conclusion, with the Parisians seeing things through for three vital points.