PSG has now won the season-opening cup on 14 separate times.
Paris Saint-Germain needed a stoppage-time leveler followed by a perfect penalty shootout to overcome their arch-rivals in Kuwait and capture a fourth straight French Super Cup title.
The European champions appeared to be coasting towards a comfortable triumph in the showdown between the Ligue 1 winners and the Coupe de France winners after Ousmane Dembele opened the scoring early on.
However, the southern French side struck two times late to seize a surprise advantage. Initially, the English forward scored from the spot-kick, before Willian Pacho unfortunately turned the ball into his own net for an own-goal.
In a remarkable twist of fortune, Goncalo Ramos grabbed a crucial equaliser in the final moments to force the contest into a deciding shootout. PSG goalkeeper Chevalier then stood as the key figure, saving crucial kicks from Matt O'Riley and Traore.
In the shootout, Goncalo Ramos, the midfielder, the full-back, and Desire Doue all scored with composure for Paris Saint-Germain to complete a convincing penalty victory.
The record winners PSG, who faced last season's Ligue 1 second-placed team Marseille after achieving a domestic double, have now won this trophy for the 12th time in the last 13 years.
