The Parisian club has now claimed the season-opening cup on 14 separate times.
Paris Saint-Germain needed a stoppage-time leveler followed by a successful penalty shootout to overcome their arch-rivals in the Gulf and secure a fourth straight French Super Cup victory.
The European champions seemed to be sailing towards a comfortable triumph in the match between the Ligue 1 winners and the Coupe de France holders after Ousmane Dembele found the scoring in the opening stages.
Yet, the southern French side struck two times late to seize a shock advantage. Initially, the English forward converted from the spot-kick, before the defender unfortunately directed the ball into his own net for an own goal.
In a remarkable turn of events, Goncalo Ramos grabbed a crucial equaliser in the final moments to force the contest into a deciding shootout. The Parisian shot-stopper Chevalier then stood as the key figure, stopping decisive attempts from Matt O'Riley and Traore.
In the shootout, Goncalo Ramos, Vitinha, Nuno Mendes, and the young talent all scored with composure for PSG to complete a convincing penalty victory.
Now 14-time winners PSG, who faced last season's Ligue 1 second-placed team Marseille after completing a league and cup double, have now lifted this competition for the twelfth time in the past thirteen seasons.