PSG has now won the prestigious trophy on 14 different occasions.
The Parisian giants needed a stoppage-time leveler followed by a successful spot-kick decider to overcome their arch-rivals in the Gulf and capture a fourth straight French Super Cup victory.
The European champions appeared to be coasting towards a straightforward triumph in the showdown featuring the Ligue 1 champions and the French Cup holders after Ousmane Dembele found the scoring early on.
Yet, the southern French side struck two times in the closing moments to seize a surprise advantage. Initially, Mason Greenwood converted from the penalty spot, before the defender inadvertently directed the ball into his own net for an own goal.
In a breathtaking twist of events, Goncalo Ramos snatched a vital leveler in the dying seconds to send the match into a penalty shootout. PSG goalkeeper Chevalier then stood as the key figure, saving decisive kicks from Matt O'Riley and Traore.
In the shootout, Ramos, Vitinha, the full-back, and Desire Doue all scored successfully for PSG to complete a 4-1 shootout win.
The record champions Paris Saint-Germain, who faced last season's Ligue 1 second-placed team Olympique de Marseille after achieving a league and cup double, have now won this trophy for the 12th time in the last thirteen years.