The Parisian club has now claimed the season-opening cup on 14 different occasions.
Paris Saint-Germain required a stoppage-time leveler followed by a perfect spot-kick decider to overcome their arch-rivals in the Gulf and secure a record-extending fourth consecutive French Super Cup victory.
The European champions appeared to be sailing towards a straightforward win in the showdown between the Ligue 1 winners and the French Cup winners after the French winger found the scoring early on.
However, the southern French side fired two times in the closing moments to take a surprise lead. First, 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 grabbed a crucial leveler in the dying seconds to send the contest into a deciding shootout. PSG goalkeeper Chevalier then emerged as the hero, stopping decisive kicks from O'Riley and Traore.
From the spot, Goncalo Ramos, the midfielder, Nuno Mendes, and Desire Doue all scored successfully for Paris Saint-Germain to complete a convincing penalty victory.
Now 14-time winners Paris Saint-Germain, who faced last season's Ligue 1 runners-up Olympique de Marseille after achieving a domestic double, have now lifted this competition for the 12th time in the past 13 years.
