The Parisian club has now claimed the prestigious trophy on fourteen different occasions.
Paris Saint-Germain needed a dramatic equaliser followed by a successful penalty shootout to overcome their arch-rivals in Kuwait and secure a fourth straight French Super Cup title.
The Champions League holders appeared to be sailing towards a straightforward triumph in the showdown featuring the French league winners and the Coupe de France holders after Ousmane Dembele found the net in the opening stages.
Yet, the southern French side struck two times late to take a shock advantage. Initially, the English forward scored from the penalty spot, before the defender inadvertently turned the ball into his own net for an own goal.
In a breathtaking turn of fortune, the Portuguese striker grabbed a vital equaliser in the dying seconds to force the match into a penalty shootout. PSG goalkeeper Chevalier then stood as the hero, stopping decisive kicks from Matt O'Riley and Hamed Traore.
From the spot, Goncalo Ramos, Vitinha, Nuno Mendes, and Desire Doue all scored with composure for PSG to complete a 4-1 penalty victory.
The record champions PSG, who met last season's Ligue 1 second-placed team Marseille after achieving a domestic double, have now lifted this competition for the twelfth time in the past 13 seasons.