The Parisian club has now secured the season-opening trophy on fourteen separate occasions.
Paris Saint-Germain required a dramatic leveler followed by a perfect spot-kick decider to overcome their arch-rivals in Kuwait and secure a record-extending fourth consecutive French Super Cup title.
The European champions seemed to be sailing towards a straightforward triumph in the match between the French league winners and the Coupe de France winners after the French winger opened the net in the opening stages.
Yet, the southern French side struck two times in the closing moments to seize a surprise lead. First, the English forward converted from the penalty spot, before Willian Pacho unfortunately directed the ball into his own net for an own-goal.
In a breathtaking turn of fortune, Goncalo Ramos grabbed a crucial leveler in the final seconds to send the match into a penalty shootout. The Parisian shot-stopper Chevalier then emerged as the hero, stopping crucial kicks from Matt O'Riley and Traore.
In the shootout, Goncalo Ramos, the midfielder, Nuno Mendes, and the young talent all scored with composure for Paris Saint-Germain to complete a convincing shootout win.
The record winners PSG, who met last season's Ligue 1 second-placed team Marseille after achieving a domestic double, have now lifted this trophy for the twelfth time in the past 13 seasons.
