The Parisian club has now secured the season-opening cup on fourteen different times.
Paris Saint-Germain needed a stoppage-time equaliser followed by a successful spot-kick decider to get past their arch-rivals in the Gulf and capture a fourth straight French Super Cup title.
The Champions League holders appeared to be sailing towards a comfortable win in the showdown featuring the French league winners and the Coupe de France winners after the French winger found the scoring early on.
However, the southern French side fired two times late to take a surprise lead. Initially, Mason Greenwood converted from the spot-kick, before Willian Pacho unfortunately directed the ball into his own net for an own goal.
In a remarkable turn of events, Goncalo Ramos grabbed a vital equaliser in the dying seconds to send the contest into a deciding shootout. The Parisian shot-stopper Chevalier then emerged as the hero, stopping decisive kicks from Matt O'Riley and Hamed Traore.
In the shootout, Goncalo Ramos, the midfielder, Nuno Mendes, and the young talent all scored successfully for PSG to seal a 4-1 shootout win.
Now 14-time winners PSG, who faced last season's Ligue 1 runners-up Marseille after achieving a league and cup double, have now won this trophy for the 12th time in the last 13 years.
