The Parisian club has now won the season-opening cup on 14 different occasions.
Paris Saint-Germain needed a stoppage-time equaliser followed by a successful penalty shootout to get past their arch-rivals in Kuwait and secure a record-extending fourth consecutive Trophee des Champions title.
The Champions League holders seemed to be coasting towards a straightforward win in the match featuring the Ligue 1 champions and the Coupe de France winners after the French winger opened the scoring in the opening stages.
Yet, the southern French side fired two times in the closing moments to seize a shock lead. First, Mason Greenwood converted from the spot-kick, before the defender inadvertently turned the ball into his own net for an own-goal.
In a remarkable twist of events, Goncalo Ramos snatched a vital leveler in the dying seconds to send the match into a deciding shootout. The Parisian shot-stopper Chevalier then stood as the hero, saving decisive attempts from Matt O'Riley and Traore.
From the spot, Goncalo Ramos, the midfielder, the full-back, and Desire Doue all converted with composure for PSG to seal a 4-1 shootout win.
Now 14-time champions PSG, who met last season's Ligue 1 second-placed team Olympique de Marseille after achieving a league and cup double, have now lifted this trophy for the 12th time in the last thirteen years.