The Parisian club has now won the prestigious cup on 14 separate occasions.
Paris Saint-Germain required a dramatic leveler followed by a perfect spot-kick decider to get past their arch-rivals in the Gulf and secure a record-extending fourth consecutive French Super Cup title.
The European champions seemed to be sailing towards a comfortable triumph in the match between the French league champions and the Coupe de France holders after Ousmane Dembele found the net early on.
However, the southern French side struck twice late to seize a surprise lead. Initially, Mason Greenwood scored 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 grabbed a vital equaliser in the final moments to send the match into a penalty shootout. The Parisian shot-stopper Chevalier then emerged as the key figure, stopping decisive kicks from Matt O'Riley and Hamed Traore.
From the spot, Goncalo Ramos, Vitinha, Nuno Mendes, and the young talent all converted with composure for Paris Saint-Germain to seal a convincing shootout win.
The record winners Paris Saint-Germain, who met last season's Ligue 1 second-placed team Olympique de Marseille after achieving a league and cup double, have now lifted this competition for the 12th time in the past 13 seasons.