The Parisian club has now won the season-opening cup on 14 separate times.
Paris Saint-Germain needed a dramatic leveler followed by a successful spot-kick decider to overcome Marseille in Kuwait and secure a record-extending fourth consecutive French Super Cup title.
The European champions appeared to be coasting towards a straightforward win in the match featuring the Ligue 1 winners and the Coupe de France winners after the French winger opened the scoring early on.
However, the southern French side struck twice in the closing moments to seize a surprise lead. Initially, Mason Greenwood scored from the spot-kick, before Willian Pacho inadvertently directed the ball into his own net for an own-goal.
In a breathtaking twist of events, Goncalo Ramos grabbed a crucial leveler in the final moments to force the match into a penalty shootout. The Parisian shot-stopper Chevalier then emerged as the key figure, saving decisive kicks from Matt O'Riley and Hamed Traore.
From the spot, Ramos, the midfielder, Nuno Mendes, and the young talent all converted successfully for PSG to seal a convincing shootout victory.
Now 14-time champions PSG, who met last season's Ligue 1 runners-up Olympique de Marseille after completing a domestic double, have now won this trophy for the 12th time in the last thirteen seasons.