PSG has now claimed the season-opening trophy on 14 different occasions.
Paris Saint-Germain needed a dramatic equaliser followed by a perfect spot-kick decider to overcome their arch-rivals in the Gulf and secure a fourth straight French Super Cup victory.
The Champions League holders appeared to be sailing towards a straightforward triumph in the match featuring the French league winners and the French Cup winners after Ousmane Dembele opened the net in the opening stages.
However, the southern French side fired two times in the closing moments to take a surprise lead. Initially, Mason Greenwood scored from the spot-kick, before Willian Pacho unfortunately turned the ball into his own net for an own goal.
In a remarkable turn of fortune, the Portuguese striker snatched a vital leveler in the final moments to send the contest into a penalty shootout. The Parisian shot-stopper Chevalier then stood as the key figure, saving decisive attempts from O'Riley and Hamed Traore.
From the spot, Goncalo Ramos, the midfielder, Nuno Mendes, and the young talent all converted with composure for Paris Saint-Germain to complete a 4-1 shootout win.
The record champions Paris Saint-Germain, who met last season's Ligue 1 second-placed team Olympique de Marseille after achieving a league and cup double, have now won this competition for the twelfth time in the last thirteen years.