The Parisian club has now won the prestigious trophy on 14 separate times.
Paris Saint-Germain needed a stoppage-time 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 coasting towards a straightforward triumph in the match between the Ligue 1 winners and the French Cup holders after Ousmane Dembele found the scoring early on.
However, the southern French side fired two times late to take a shock advantage. First, 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 turn of events, the Portuguese striker grabbed a vital leveler in the final seconds to send the match into a deciding shootout. The Parisian shot-stopper Chevalier then emerged as the key figure, saving decisive attempts from O'Riley and Hamed Traore.
From the spot, Goncalo Ramos, the midfielder, the full-back, and Desire Doue all converted successfully for PSG to seal a convincing shootout win.
The record winners Paris Saint-Germain, who faced last season's Ligue 1 runners-up Olympique de Marseille after achieving a league and cup double, have now won this trophy for the twelfth time in the past thirteen seasons.
