PSG has now claimed the season-opening cup on 14 separate occasions.
Paris Saint-Germain required a stoppage-time equaliser followed by a successful penalty shootout to overcome their arch-rivals in Kuwait and secure a fourth straight French Super Cup title.
The European champions seemed to be coasting towards a straightforward triumph in the showdown featuring the Ligue 1 champions and the Coupe de France holders after the French winger found the net in the opening stages.
Yet, the southern French side fired two times late to take a surprise advantage. First, Mason Greenwood scored from the spot-kick, before the defender unfortunately directed the ball into his own net for an own goal.
In a breathtaking turn of events, Goncalo Ramos grabbed a vital equaliser in the final moments to force the match into a deciding shootout. The Parisian shot-stopper Chevalier then stood as the hero, stopping crucial attempts from Matt O'Riley and Hamed Traore.
From the spot, Ramos, Vitinha, the full-back, and the young talent all converted with composure for PSG to seal a convincing penalty victory.
Now 14-time champions PSG, who met last season's Ligue 1 runners-up Olympique de Marseille after completing a league and cup double, have now lifted this trophy for the twelfth time in the last thirteen years.