PSG has now secured the season-opening trophy on 14 different times.
The Parisian giants needed a dramatic leveler followed by a perfect penalty shootout to overcome their arch-rivals in the Gulf and secure a fourth straight French Super Cup title.
The Champions League holders seemed to be coasting towards a straightforward win in the match featuring the French league champions and the French Cup winners after the French winger opened the scoring early on.
However, the southern French side struck two times late to seize a surprise advantage. Initially, the English forward converted from the spot-kick, before Willian Pacho inadvertently directed the ball into his own net for an own-goal.
In a breathtaking turn of fortune, the Portuguese striker snatched a vital equaliser in the final moments to send the contest into a penalty shootout. PSG goalkeeper Chevalier then emerged as the hero, stopping decisive kicks from Matt O'Riley and Traore.
In the shootout, Goncalo Ramos, the midfielder, Nuno Mendes, and the young talent all converted successfully for PSG to complete a convincing penalty victory.
The record champions PSG, who met last season's Ligue 1 second-placed team Olympique de Marseille after completing a domestic double, have now won this trophy for the twelfth time in the last 13 seasons.