The Parisian club has now claimed the season-opening trophy on 14 separate times.
Paris Saint-Germain required a dramatic leveler followed by a successful spot-kick decider to get past their arch-rivals in the Gulf and capture a fourth straight French Super Cup victory.
The European champions appeared to be sailing towards a straightforward triumph in the match featuring the French league champions and the French Cup winners after the French winger opened the net in the opening stages.
However, the southern French side struck twice late to take a shock advantage. First, Mason Greenwood converted from the penalty spot, before Willian Pacho unfortunately directed the ball into his own net for an own-goal.
In a remarkable turn of fortune, Goncalo Ramos snatched a crucial equaliser in the dying moments to force the contest into a penalty shootout. PSG goalkeeper Chevalier then stood as the key figure, stopping crucial kicks from Matt O'Riley and Hamed Traore.
In the shootout, Ramos, the midfielder, the full-back, and the young talent all converted with composure for PSG to seal a convincing shootout win.
Now 14-time champions PSG, who met last season's Ligue 1 runners-up Olympique de Marseille after completing a league and cup double, have now lifted this competition for the twelfth time in the last 13 seasons.