The Parisian club has now secured the season-opening trophy on 14 separate times.
Paris Saint-Germain required a stoppage-time equaliser followed by a perfect spot-kick decider to overcome their arch-rivals in the Gulf and capture a fourth straight French Super Cup victory.
The European champions seemed to be coasting towards a comfortable triumph in the match featuring the Ligue 1 champions and the Coupe de France winners after the French winger opened the net in the opening stages.
However, the southern French side struck two times in the closing moments to seize a surprise lead. Initially, Mason Greenwood converted from the spot-kick, before the defender inadvertently directed the ball into his own net for an own goal.
In a breathtaking turn of events, Goncalo Ramos grabbed a vital equaliser in the dying seconds to force the contest into a penalty shootout. PSG goalkeeper Chevalier then stood as the key figure, saving crucial attempts from Matt O'Riley and Hamed Traore.
In the shootout, Goncalo Ramos, Vitinha, the full-back, and Desire Doue all converted with composure for PSG to seal a 4-1 shootout victory.
Now 14-time winners PSG, who faced last season's Ligue 1 second-placed team Olympique de Marseille after completing a league and cup double, have now won this trophy for the 12th time in the last thirteen years.
