PSG has now won the season-opening cup on 14 separate occasions.
Paris Saint-Germain required a stoppage-time leveler followed by a perfect penalty shootout to get past their arch-rivals in Kuwait and capture a fourth straight French Super Cup title.
The European champions appeared to be coasting towards a straightforward triumph in the match between the French league champions and the Coupe de France holders after the French winger opened the net early on.
However, the southern French side fired two times in the closing moments to seize a shock lead. First, Mason Greenwood scored from the penalty spot, before the defender unfortunately directed the ball into his own net for an own goal.
In a breathtaking turn of fortune, Goncalo Ramos grabbed a crucial leveler in the dying moments to force the match into a penalty shootout. The Parisian shot-stopper Lucas Chevalier then emerged as the hero, saving decisive attempts from Matt O'Riley and Traore.
From the spot, Goncalo Ramos, Vitinha, the full-back, and Desire Doue all converted with composure for Paris Saint-Germain to seal a 4-1 penalty victory.
Now 14-time winners Paris Saint-Germain, who met last season's Ligue 1 runners-up Olympique de Marseille after achieving a league and cup double, have now lifted this trophy for the twelfth time in the last 13 seasons.
