PSG has now won the season-opening cup on 14 different occasions.
Paris Saint-Germain needed a dramatic equaliser followed by a successful spot-kick decider to get past their arch-rivals in the Gulf and capture a fourth straight French Super Cup victory.
The Champions League holders appeared to be coasting towards a comfortable triumph in the match featuring the French league champions and the Coupe de France holders after Ousmane Dembele opened the net early on.
However, the southern French side struck twice late to seize a surprise advantage. First, the English forward converted from the spot-kick, before the defender inadvertently directed the ball into his own net for an own goal.
In a remarkable twist of events, Goncalo Ramos snatched a crucial leveler in the final seconds to force the contest into a deciding shootout. The Parisian shot-stopper Chevalier then emerged as the hero, saving decisive kicks 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 seal a convincing shootout win.
Now 14-time winners Paris Saint-Germain, who met last season's Ligue 1 runners-up Olympique de Marseille after completing a domestic double, have now lifted this trophy for the twelfth time in the past 13 years.
