PSG has now won the season-opening trophy on fourteen different occasions.
Paris Saint-Germain required a stoppage-time equaliser followed by a perfect penalty shootout to overcome their arch-rivals in Kuwait and secure a record-extending fourth consecutive French Super Cup title.
The European champions seemed to be sailing towards a straightforward win in the match featuring the Ligue 1 winners and the Coupe de France holders after Ousmane Dembele opened the net early on.
However, the southern French side fired twice late to take a surprise lead. Initially, Mason Greenwood scored from the spot-kick, before the defender inadvertently turned the ball into his own net for an own goal.
In a remarkable twist of fortune, Goncalo Ramos grabbed a crucial leveler in the final moments to send the match into a penalty shootout. The Parisian shot-stopper Chevalier then emerged as the hero, saving decisive kicks from Matt O'Riley and Traore.
From the spot, Goncalo Ramos, Vitinha, the full-back, and Desire Doue all converted successfully for Paris Saint-Germain to seal a 4-1 penalty win.
Now 14-time winners Paris Saint-Germain, who met last season's Ligue 1 runners-up Olympique de Marseille after completing a league and cup double, have now lifted this trophy for the 12th time in the past 13 seasons.