PSG has now secured the prestigious trophy on 14 different occasions.
Paris Saint-Germain required a dramatic leveler followed by a perfect spot-kick decider to get past their arch-rivals in the Gulf and capture a record-extending fourth consecutive French Super Cup title.
The Champions League holders appeared to be coasting towards a comfortable win in the match featuring the Ligue 1 champions and the Coupe de France winners after Ousmane Dembele found the net in the opening stages.
However, the southern French side struck twice late to take a shock advantage. Initially, 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 fortune, the Portuguese striker grabbed a crucial equaliser in the final moments to force the contest into a penalty shootout. PSG goalkeeper Chevalier then emerged as the hero, saving decisive attempts from Matt O'Riley and Hamed Traore.
In the shootout, Goncalo Ramos, the midfielder, Nuno Mendes, and the young talent all converted successfully for PSG to seal a 4-1 penalty victory.
The record champions Paris Saint-Germain, who met last season's Ligue 1 second-placed team Marseille after achieving a domestic double, have now won this trophy for the 12th time in the last thirteen years.