The Parisian club has now secured the season-opening cup on fourteen separate occasions.
Paris Saint-Germain required a dramatic leveler followed by a successful spot-kick decider to get past their arch-rivals in Kuwait and capture a fourth straight French Super Cup victory.
The Champions League holders appeared to be sailing towards a straightforward win in the showdown between the Ligue 1 champions and the French Cup winners after Ousmane Dembele found the net early on.
Yet, the southern French side fired twice late to take a shock advantage. Initially, Mason Greenwood scored from the penalty spot, before Willian Pacho unfortunately turned the ball into his own net for an own goal.
In a remarkable twist of fortune, the Portuguese striker grabbed a crucial equaliser in the final moments to send the match into a penalty shootout. The Parisian shot-stopper Chevalier then emerged as the key figure, saving decisive attempts from Matt O'Riley and Hamed Traore.
From the spot, Goncalo Ramos, the midfielder, the full-back, and Desire Doue all scored with composure for Paris Saint-Germain to seal a 4-1 penalty win.
The record winners Paris Saint-Germain, who met last season's Ligue 1 runners-up Marseille after completing a domestic double, have now lifted this trophy for the twelfth time in the last thirteen seasons.