The Parisian club has now won the prestigious trophy on 14 different occasions.
Paris Saint-Germain required a stoppage-time leveler followed by a perfect spot-kick decider to overcome their arch-rivals in the Gulf and secure a record-extending fourth consecutive French Super Cup victory.
The Champions League holders appeared to be sailing towards a straightforward win in the showdown between the French league winners and the French Cup winners after Ousmane Dembele found the scoring early on.
However, the southern French side struck twice late to take a surprise lead. Initially, the English forward scored from the spot-kick, before Willian Pacho inadvertently turned the ball into his own net for an own goal.
In a breathtaking turn of fortune, the Portuguese striker snatched a crucial leveler in the dying seconds to force the contest into a penalty shootout. The Parisian shot-stopper Chevalier then stood as the key figure, saving decisive attempts from Matt O'Riley and Traore.
From the spot, Goncalo Ramos, the midfielder, the full-back, and Desire Doue all converted with composure for Paris Saint-Germain to seal a 4-1 penalty win.
Now 14-time champions Paris Saint-Germain, who faced last season's Ligue 1 second-placed team Olympique de Marseille after achieving a domestic double, have now lifted this competition for the twelfth time in the past thirteen seasons.
