PSG has now secured the prestigious cup on 14 different times.
The Parisian giants required a stoppage-time leveler followed by a successful spot-kick decider to get past their arch-rivals in Kuwait and secure a record-extending fourth consecutive French Super Cup title.
The Champions League holders appeared to be coasting towards a comfortable win in the showdown featuring the Ligue 1 winners and the Coupe de France holders after Ousmane Dembele opened the scoring early on.
However, the southern French side struck twice late to seize a shock lead. First, Mason Greenwood converted from the penalty spot, before the defender unfortunately directed the ball into his own net for an own goal.
In a breathtaking turn of fortune, Goncalo Ramos grabbed a vital leveler in the dying seconds to force the match into a deciding shootout. PSG goalkeeper Chevalier then emerged as the key figure, stopping crucial attempts from Matt O'Riley and Traore.
From the spot, Ramos, the midfielder, Nuno Mendes, and Desire Doue all converted with composure for Paris Saint-Germain to complete a convincing shootout win.
The record champions Paris Saint-Germain, who faced last season's Ligue 1 second-placed team Olympique de Marseille after completing a domestic double, have now lifted this competition for the twelfth time in the last thirteen seasons.
