The Parisian club has now won the season-opening trophy on fourteen different times.
Paris Saint-Germain required a dramatic leveler followed by a successful penalty shootout to get past their arch-rivals in Kuwait and capture a fourth straight French Super Cup title.
The Champions League holders appeared to be coasting towards a straightforward win in the match between the Ligue 1 winners and the Coupe de France holders after the French winger opened the scoring in the opening stages.
However, the southern French side fired two times late to seize a surprise advantage. Initially, the English forward scored from the spot-kick, before the defender unfortunately turned the ball into his own net for an own-goal.
In a breathtaking turn of events, Goncalo Ramos grabbed a vital leveler in the dying moments to force the match into a penalty shootout. The Parisian shot-stopper Chevalier then stood as the key figure, stopping decisive attempts from Matt O'Riley and Hamed Traore.
In the shootout, Goncalo Ramos, Vitinha, Nuno Mendes, and Desire Doue all converted with composure for PSG to complete a 4-1 shootout victory.
Now 14-time champions PSG, who met last season's Ligue 1 second-placed team Marseille after completing a domestic double, have now lifted this trophy for the twelfth time in the last 13 seasons.