The Parisian club has now secured the prestigious trophy on 14 separate times.
Paris Saint-Germain needed a dramatic leveler followed by a perfect spot-kick decider to overcome their arch-rivals in the Gulf and capture a record-extending fourth consecutive French Super Cup victory.
The European champions appeared to be sailing towards a straightforward win in the showdown between the Ligue 1 champions and the French Cup winners after Ousmane Dembele opened the net early on.
Yet, the southern French side struck twice late to seize a shock advantage. Initially, the English forward scored from the penalty spot, before Willian Pacho unfortunately directed the ball into his own net for an own-goal.
In a remarkable twist of fortune, the Portuguese striker snatched a vital equaliser in the dying seconds to force the match into a deciding shootout. The Parisian shot-stopper Chevalier then stood as the hero, stopping crucial attempts from Matt O'Riley and Traore.
In the shootout, Ramos, the midfielder, Nuno Mendes, and Desire Doue all scored with composure for Paris Saint-Germain to seal a 4-1 shootout victory.
The record winners PSG, who met last season's Ligue 1 second-placed team Marseille after achieving a domestic double, have now lifted this trophy for the twelfth time in the last 13 years.