The Parisian club has now won the prestigious cup on 14 separate occasions.
Paris Saint-Germain needed a stoppage-time leveler followed by a perfect spot-kick decider to get past their arch-rivals in Kuwait and secure a record-extending fourth consecutive French Super Cup victory.
The European champions seemed to be sailing towards a straightforward triumph in the showdown featuring the French league winners and the French Cup holders after Ousmane Dembele found the net in the opening stages.
Yet, the southern French side struck twice late to take a shock lead. Initially, the English forward scored from the spot-kick, before the defender unfortunately directed the ball into his own net for an own-goal.
In a remarkable twist of events, the Portuguese striker snatched a crucial equaliser in the dying seconds to force the match into a penalty shootout. The Parisian shot-stopper Chevalier then stood as the key figure, saving crucial kicks from O'Riley and Hamed Traore.
In the shootout, Ramos, Vitinha, Nuno Mendes, and the young talent all converted successfully for PSG to seal a 4-1 penalty victory.
The record winners Paris Saint-Germain, who faced last season's Ligue 1 second-placed team Marseille after achieving a domestic double, have now won this competition for the twelfth time in the last 13 years.