The Parisian club has now claimed the season-opening cup on 14 different times.
The Parisian giants required a stoppage-time equaliser followed by a successful spot-kick decider to overcome their arch-rivals in Kuwait and capture a record-extending fourth consecutive Trophee des Champions victory.
The Champions League holders appeared to be sailing towards a comfortable win in the showdown between the Ligue 1 winners and the Coupe de France holders after the French winger found the net early on.
However, Marseille struck twice in the closing moments to seize a surprise advantage. First, the English forward converted from the spot-kick, before the defender inadvertently directed the ball into his own net for an own goal.
In a remarkable twist of fortune, Goncalo Ramos snatched a vital leveler in the dying moments to send the match 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, Ramos, Vitinha, the full-back, and Desire Doue all scored with composure for PSG to seal a 4-1 penalty win.
Now 14-time winners PSG, who met last season's Ligue 1 runners-up Marseille after completing a domestic double, have now lifted this competition for the twelfth time in the last 13 years.
