The Parisian club has now won the prestigious cup on 14 separate times.
Paris Saint-Germain required a dramatic leveler followed by a perfect penalty shootout to overcome their arch-rivals in the Gulf and secure a record-extending fourth consecutive French Super Cup victory.
The Champions League holders seemed 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 scoring early on.
Yet, the southern French side struck twice in the closing moments to seize a surprise lead. 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 vital equaliser in the final seconds to force the contest into a deciding shootout. PSG goalkeeper Chevalier then emerged as the hero, saving decisive attempts from Matt O'Riley and Traore.
From the spot, Ramos, the midfielder, the full-back, and Desire Doue all converted with composure for Paris Saint-Germain to complete a 4-1 penalty victory.
The record winners PSG, who faced last season's Ligue 1 runners-up Marseille after completing a domestic double, have now won this competition for the twelfth time in the past thirteen seasons.