The Parisian club has now won the season-opening cup on 14 different times.
The Parisian giants needed a stoppage-time leveler followed by a successful penalty shootout to get past their arch-rivals in Kuwait and secure a record-extending fourth consecutive French Super Cup title.
The European champions appeared to be sailing towards a comfortable win in the showdown between the Ligue 1 champions and the Coupe de France holders after Ousmane Dembele found the net early on.
However, the southern French side struck twice late to seize a surprise lead. First, Mason Greenwood scored from the penalty spot, before Willian Pacho inadvertently directed the ball into his own net for an own goal.
In a breathtaking twist of fortune, Goncalo Ramos grabbed a crucial equaliser in the final moments to send the match into a penalty shootout. PSG goalkeeper Chevalier then stood as the hero, stopping crucial kicks from Matt O'Riley and Traore.
From the spot, Goncalo Ramos, the midfielder, Nuno Mendes, and Desire Doue all scored with composure for PSG to complete a 4-1 shootout victory.
Now 14-time champions Paris Saint-Germain, who met last season's Ligue 1 runners-up Marseille after achieving a domestic double, have now won this trophy for the twelfth time in the past 13 seasons.