The Parisian club has now secured the prestigious trophy on 14 separate times.
Paris Saint-Germain required a stoppage-time leveler followed by a successful spot-kick decider to overcome their arch-rivals in Kuwait and secure a fourth straight French Super Cup victory.
The European champions seemed to be sailing towards a comfortable win in the match featuring the Ligue 1 winners and the Coupe de France holders after the French winger opened the scoring in the opening stages.
However, Marseille struck two times late to take a surprise advantage. Initially, the English forward converted from the penalty spot, before Willian Pacho inadvertently turned the ball into his own net for an own goal.
In a breathtaking twist of fortune, Goncalo Ramos snatched a crucial equaliser in the dying moments to force the contest into a deciding shootout. The Parisian shot-stopper Chevalier then emerged as the key figure, stopping decisive kicks from Matt O'Riley and Traore.
From the spot, Ramos, Vitinha, the full-back, and Desire Doue all converted successfully for PSG to complete 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 domestic double, have now won this competition for the 12th time in the last 13 years.
