PSG has now secured the season-opening trophy on fourteen different occasions.
The Parisian giants required a dramatic leveler followed by a successful spot-kick decider to get past Marseille in Kuwait and capture a fourth straight French Super Cup victory.
The European champions appeared to be sailing towards a comfortable win in the match featuring the Ligue 1 champions and the Coupe de France winners after the French winger found the net in the opening stages.
However, Marseille struck two times late to seize a surprise lead. First, Mason Greenwood scored from the penalty spot, before the defender unfortunately turned the ball into his own net for an own goal.
In a remarkable twist of fortune, Goncalo Ramos grabbed a vital leveler in the final seconds to force the contest into a penalty shootout. The Parisian shot-stopper Chevalier then stood as the hero, saving decisive attempts from Matt O'Riley and Traore.
In the shootout, Goncalo Ramos, the midfielder, the full-back, and Desire Doue all converted with composure for Paris Saint-Germain to complete a convincing penalty victory.
The record champions PSG, who faced 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 past 13 years.