The Parisian club has now claimed the season-opening cup on fourteen different times.
Paris Saint-Germain required a stoppage-time equaliser followed by a successful spot-kick decider to overcome their arch-rivals in Kuwait and capture a fourth straight French Super Cup title.
The Champions League holders seemed to be coasting towards a comfortable win in the showdown between the Ligue 1 champions and the French Cup holders after the French winger found the net early on.
Yet, the southern French side fired two times in the closing moments to take a shock lead. First, Mason Greenwood converted from the spot-kick, before Willian Pacho unfortunately turned the ball into his own net for an own goal.
In a breathtaking twist of events, the Portuguese striker grabbed a crucial leveler in the final moments to send the contest into a deciding shootout. The Parisian shot-stopper Chevalier then emerged as the key figure, stopping decisive kicks from O'Riley and Traore.
From the spot, Ramos, Vitinha, the full-back, and the young talent all converted with composure for Paris Saint-Germain to seal a convincing penalty victory.
The record champions PSG, who met last season's Ligue 1 runners-up Marseille after completing a league and cup double, have now lifted this competition for the twelfth time in the last thirteen years.