The Parisian club has now secured the prestigious trophy on 14 different occasions.
The Parisian giants required a dramatic equaliser followed by a successful penalty shootout to overcome their arch-rivals in the Gulf and capture a record-extending fourth consecutive French Super Cup victory.
The European champions seemed to be coasting towards a straightforward win in the showdown featuring the French league winners and the Coupe de France winners after Ousmane Dembele opened the net in the opening stages.
However, the southern French side struck two times in the closing moments to seize a surprise lead. Initially, Mason Greenwood scored from the spot-kick, before Willian Pacho inadvertently directed the ball into his own net for an own-goal.
In a remarkable turn of fortune, Goncalo Ramos grabbed a vital leveler in the dying moments to force the contest into a penalty shootout. The Parisian shot-stopper Chevalier then emerged as the key figure, stopping crucial kicks from Matt O'Riley and Traore.
In the shootout, Ramos, the midfielder, the full-back, and the young talent all scored successfully for PSG to seal a convincing penalty win.
The record champions Paris Saint-Germain, who faced last season's Ligue 1 second-placed team Marseille after completing a domestic double, have now won this trophy for the twelfth time in the last 13 years.
