The Parisian club has now claimed the season-opening cup on 14 separate times.
Paris Saint-Germain needed 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 victory.
The European champions seemed to be coasting towards a comfortable win in the showdown between the Ligue 1 champions and the Coupe de France winners after the French winger found the scoring in the opening stages.
Yet, the southern French side struck two times in the closing moments to take a shock advantage. First, Mason Greenwood scored from the spot-kick, before Willian Pacho inadvertently turned the ball into his own net for an own goal.
In a breathtaking turn of events, the Portuguese striker snatched a vital equaliser in the final seconds to force the match into a deciding shootout. The Parisian shot-stopper Lucas Chevalier then emerged as the hero, saving crucial kicks from Matt O'Riley and Traore.
From the spot, Goncalo Ramos, the midfielder, Nuno Mendes, and Desire Doue all converted with composure for PSG to complete a 4-1 shootout victory.
Now 14-time champions Paris Saint-Germain, who met last season's Ligue 1 second-placed team Marseille after completing a domestic double, have now lifted this trophy for the twelfth time in the past 13 seasons.
