The Parisian club has now won the prestigious trophy on fourteen separate occasions.
Paris Saint-Germain needed a stoppage-time equaliser followed by a successful penalty shootout to get past their arch-rivals in the Gulf and secure a record-extending fourth consecutive French Super Cup victory.
The European champions appeared to be coasting towards a straightforward win in the match featuring the Ligue 1 champions and the French Cup holders after Ousmane Dembele opened the net early on.
Yet, the southern French side struck twice late to seize a surprise advantage. First, the English forward converted from the spot-kick, before Willian Pacho inadvertently directed the ball into his own net for an own-goal.
In a remarkable turn of events, Goncalo Ramos snatched a crucial equaliser in the final seconds to send the contest into a deciding shootout. PSG goalkeeper Chevalier then emerged as the key figure, stopping crucial attempts from Matt O'Riley and Hamed Traore.
From the spot, Goncalo Ramos, Vitinha, the full-back, and Desire Doue all converted successfully for Paris Saint-Germain to complete a convincing penalty victory.
The record winners PSG, who met last season's Ligue 1 second-placed team Olympique de Marseille after completing a domestic double, have now lifted this competition for the twelfth time in the past 13 seasons.