PSG has now claimed the season-opening cup on 14 separate times.
The Parisian giants needed a dramatic leveler followed by a successful spot-kick decider to overcome their arch-rivals in Kuwait and secure a fourth straight Trophee des Champions victory.
The European champions appeared to be coasting towards a comfortable triumph in the showdown between the French league champions and the Coupe de France holders after Ousmane Dembele found the scoring in the opening stages.
However, Marseille struck two times in the closing moments to seize a surprise advantage. First, the English forward scored from the penalty spot, before the defender inadvertently turned the ball into his own net for an own goal.
In a breathtaking twist of fortune, the Portuguese striker snatched a vital equaliser in the final moments to send the contest into a penalty shootout. The Parisian shot-stopper Chevalier then emerged as the key figure, stopping crucial kicks from Matt O'Riley and Traore.
In the shootout, Goncalo Ramos, the midfielder, Nuno Mendes, and Desire Doue all scored successfully for Paris Saint-Germain to complete a 4-1 shootout win.
The record champions PSG, who met last season's Ligue 1 second-placed team Marseille after completing a league and cup double, have now won this competition for the 12th time in the last thirteen seasons.
