PSG has now won the prestigious trophy on 14 different times.
The Parisian giants needed a stoppage-time leveler followed by a perfect penalty shootout to overcome their arch-rivals in Kuwait and capture a fourth straight French Super Cup victory.
The European champions appeared to be coasting towards a straightforward win in the match featuring the French league winners and the Coupe de France holders after the French winger opened the scoring early on.
Yet, Marseille fired two times late to seize a shock lead. Initially, Mason Greenwood converted from the penalty spot, before Willian Pacho unfortunately turned the ball into his own net for an own-goal.
In a remarkable twist of fortune, the Portuguese striker grabbed a vital leveler in the final moments to send 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, Goncalo Ramos, Vitinha, the full-back, and Desire Doue all converted successfully for PSG to complete a convincing penalty victory.
The record champions PSG, 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 last thirteen years.