The Parisian club has now claimed the season-opening cup on fourteen different times.
Paris Saint-Germain needed a stoppage-time leveler followed by a successful spot-kick decider to get past their arch-rivals in Kuwait and capture a fourth straight French Super Cup victory.
The Champions League holders seemed to be coasting towards a straightforward triumph in the match between the Ligue 1 winners and the Coupe de France holders after the French winger found the scoring early on.
Yet, the southern French side struck twice late to take a surprise lead. Initially, the English forward scored from the spot-kick, before Willian Pacho unfortunately turned the ball into his own net for an own goal.
In a remarkable twist of events, the Portuguese striker grabbed a crucial leveler in the final moments to force the match into a deciding shootout. PSG goalkeeper Chevalier then emerged as the key figure, stopping decisive attempts from Matt O'Riley and Traore.
From the spot, Ramos, the midfielder, the full-back, and the young talent all scored with composure for Paris Saint-Germain to seal a 4-1 shootout win.
Now 14-time winners PSG, who faced last season's Ligue 1 second-placed team Marseille after completing a league and cup double, have now won this trophy for the 12th time in the past 13 years.