PSG has now secured the season-opening cup on 14 different occasions.
The Parisian giants needed a stoppage-time leveler followed by a perfect spot-kick decider to get past their arch-rivals in Kuwait and capture a record-extending fourth consecutive Trophee des Champions title.
The Champions League holders appeared to be coasting towards a comfortable triumph in the showdown between the French league champions and the Coupe de France holders after the French winger opened the scoring in the opening stages.
However, the southern French side struck twice late to take a shock advantage. Initially, the English forward 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 snatched a crucial equaliser in the dying seconds to force the match into a penalty shootout. The Parisian shot-stopper Chevalier then stood as the hero, saving decisive kicks from Matt O'Riley and Traore.
In the shootout, Ramos, Vitinha, the full-back, and the young talent all converted successfully for Paris Saint-Germain to seal a 4-1 shootout win.
The record champions PSG, who faced last season's Ligue 1 second-placed team Marseille after achieving a league and cup double, have now lifted this competition for the twelfth time in the past 13 seasons.
