PSG has now secured the season-opening trophy on 14 separate occasions.
The Parisian giants required a stoppage-time leveler followed by a successful penalty shootout to get past their arch-rivals in Kuwait and secure a record-extending fourth consecutive French Super Cup victory.
The Champions League holders appeared to be coasting towards a straightforward win in the match between the Ligue 1 champions and the French Cup winners after the French winger opened the scoring early on.
However, Marseille struck two times in the closing moments to seize a surprise advantage. Initially, Mason Greenwood scored from the spot-kick, before the defender unfortunately directed the ball into his own net for an own goal.
In a remarkable twist of events, Goncalo Ramos snatched a vital leveler in the final seconds to force the contest into a deciding shootout. The Parisian shot-stopper Chevalier then stood as the key figure, saving crucial kicks from Matt O'Riley and Traore.
From the spot, Ramos, the midfielder, the full-back, and the young talent all scored successfully for Paris Saint-Germain to complete a convincing penalty victory.
The record winners Paris Saint-Germain, who faced last season's Ligue 1 runners-up Marseille after completing a domestic double, have now won this competition for the 12th time in the past 13 years.