PSG has now won the prestigious cup on fourteen different occasions.
The Parisian giants needed a dramatic leveler followed by a successful spot-kick decider to overcome their arch-rivals in Kuwait and capture a record-extending fourth consecutive French Super Cup victory.
The European champions appeared to be coasting towards a straightforward triumph in the showdown between the Ligue 1 winners and the French Cup holders after the French winger found the scoring early on.
However, Marseille fired twice late to seize a surprise lead. First, 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 turn of events, Goncalo Ramos grabbed a crucial equaliser in the final seconds to force the contest into a penalty shootout. PSG goalkeeper Chevalier then stood as the key figure, stopping crucial kicks from Matt O'Riley and Traore.
From the spot, Goncalo Ramos, the midfielder, Nuno Mendes, and the young talent all converted with composure for Paris Saint-Germain to seal a 4-1 penalty victory.
The record winners Paris Saint-Germain, who met last season's Ligue 1 runners-up Olympique de Marseille after achieving a league and cup double, have now lifted this competition for the 12th time in the past thirteen seasons.