PSG has now secured the season-opening cup on 14 different times.
The Parisian giants needed a stoppage-time leveler followed by a successful 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 triumph in the showdown between the French league winners and the Coupe de France holders after the French winger found the scoring early on.
However, the southern French side fired two times in the closing moments to seize a surprise lead. First, the English forward scored from the penalty spot, before the defender inadvertently turned the ball into his own net for an own goal.
In a breathtaking twist of events, Goncalo Ramos grabbed a vital equaliser in the dying seconds to force the contest into a deciding shootout. The Parisian shot-stopper Chevalier then stood as the hero, saving decisive kicks from Matt O'Riley and Hamed Traore.
In the shootout, Ramos, Vitinha, the full-back, and the young talent all converted successfully for PSG to complete a convincing penalty win.
Now 14-time champions Paris Saint-Germain, who met last season's Ligue 1 runners-up Olympique de Marseille after achieving a league and cup double, have now won this trophy for the 12th time in the last thirteen years.
