PSG has now won the season-opening trophy on 14 separate occasions.
Paris Saint-Germain required a stoppage-time equaliser followed by a perfect spot-kick decider to get past their arch-rivals in Kuwait and secure a record-extending fourth consecutive French Super Cup victory.
The European champions appeared to be sailing towards a comfortable triumph in the match featuring the Ligue 1 winners and the French Cup holders after the French winger opened the scoring in the opening stages.
However, the southern French side fired two times late to take a shock lead. Initially, the English forward scored from the spot-kick, before the defender inadvertently directed the ball into his own net for an own goal.
In a breathtaking twist of events, Goncalo Ramos snatched a vital equaliser in the dying moments to force the match into a deciding shootout. The Parisian shot-stopper Chevalier then emerged as the hero, stopping decisive kicks from O'Riley and Hamed Traore.
In the shootout, Goncalo Ramos, the midfielder, the full-back, and the young talent all scored successfully for Paris Saint-Germain to complete a 4-1 shootout victory.
Now 14-time winners Paris Saint-Germain, who met last season's Ligue 1 runners-up Olympique de Marseille after completing a domestic double, have now lifted this competition for the twelfth time in the last 13 seasons.