The Parisian club has now claimed the season-opening trophy on fourteen separate occasions.
Paris Saint-Germain required a dramatic leveler followed by a perfect spot-kick decider to get past their arch-rivals in Kuwait and capture a record-extending fourth consecutive French Super Cup victory.
The European champions appeared to be coasting towards a comfortable win in the match between the French league champions and the French Cup holders after Ousmane Dembele found the scoring in the opening stages.
Yet, Marseille fired twice in the closing moments to seize a shock lead. First, Mason Greenwood converted from the penalty spot, before the defender unfortunately turned the ball into his own net for an own goal.
In a remarkable twist of events, Goncalo Ramos grabbed a crucial equaliser in the dying seconds to send the contest into a deciding shootout. The Parisian shot-stopper Chevalier then emerged as the hero, stopping crucial kicks from Matt O'Riley and Traore.
In the shootout, Ramos, the midfielder, Nuno Mendes, and Desire Doue all scored successfully for PSG to complete a convincing shootout win.
Now 14-time champions PSG, who met last season's Ligue 1 second-placed team Olympique de Marseille after completing a domestic double, have now won this trophy for the twelfth time in the past thirteen years.
