PSG has now claimed the season-opening cup on fourteen different occasions.
The Parisian giants needed a stoppage-time equaliser followed by a perfect penalty shootout to overcome their arch-rivals in Kuwait and capture a fourth straight French Super Cup title.
The Champions League holders seemed to be sailing towards a straightforward triumph in the showdown featuring the French league winners and the French Cup winners after the French winger opened the net in the opening stages.
However, the southern French side struck two times late to take a surprise lead. Initially, the English forward converted from the spot-kick, before Willian Pacho unfortunately directed the ball into his own net for an own goal.
In a breathtaking twist of fortune, the Portuguese striker grabbed a vital leveler in the final seconds to force the match into a penalty shootout. The Parisian shot-stopper Chevalier then stood as the key figure, saving decisive kicks from Matt O'Riley and Traore.
In the shootout, Goncalo Ramos, Vitinha, the full-back, and Desire Doue all scored with composure for PSG to seal a convincing shootout win.
The record winners PSG, who met last season's Ligue 1 runners-up Marseille after achieving a league and cup double, have now won this trophy for the twelfth time in the past 13 seasons.
