The Parisian club has now won the prestigious cup on fourteen separate occasions.
Paris Saint-Germain needed a stoppage-time equaliser followed by a perfect spot-kick decider to overcome their arch-rivals in Kuwait and capture a fourth straight French Super Cup victory.
The European champions appeared to be coasting towards a comfortable triumph in the match between the French league champions and the French Cup holders after the French winger found the net in the opening stages.
However, the southern French side fired two times in the closing moments to seize a shock advantage. First, the English forward converted from the penalty spot, before the defender unfortunately directed the ball into his own net for an own-goal.
In a breathtaking turn of events, the Portuguese striker grabbed a vital leveler in the final moments to send the contest into a deciding shootout. The Parisian shot-stopper Chevalier then emerged as the hero, saving decisive kicks from Matt O'Riley and Traore.
From the spot, Goncalo Ramos, the midfielder, Nuno Mendes, and Desire Doue all scored successfully for Paris Saint-Germain to complete a 4-1 shootout win.
Now 14-time champions Paris Saint-Germain, who met last season's Ligue 1 runners-up Marseille after achieving a league and cup double, have now lifted this competition for the twelfth time in the past 13 years.
