The Parisian club has now claimed the prestigious trophy on fourteen different occasions.
Paris Saint-Germain needed a stoppage-time leveler followed by a successful spot-kick decider to get past their arch-rivals in Kuwait and secure a fourth straight French Super Cup victory.
The European champions appeared to be sailing towards a comfortable triumph in the match featuring the French league winners and the French Cup winners after Ousmane Dembele opened the net early on.
Yet, the southern French side struck twice in the closing moments to seize a surprise lead. First, Mason Greenwood converted from the spot-kick, before Willian Pacho inadvertently directed the ball into his own net for an own-goal.
In a breathtaking twist of events, Goncalo Ramos grabbed a vital equaliser in the dying moments to force the contest into a penalty shootout. The Parisian shot-stopper Chevalier then emerged as the key figure, saving crucial attempts from O'Riley and Traore.
In the shootout, Ramos, the midfielder, Nuno Mendes, and Desire Doue all scored with composure for Paris Saint-Germain to complete a 4-1 penalty victory.
The record winners Paris Saint-Germain, who faced last season's Ligue 1 second-placed team Olympique de Marseille after completing a domestic double, have now lifted this competition for the 12th time in the past 13 years.