The Parisian club has now claimed the season-opening trophy on 14 separate times.
Paris Saint-Germain required a stoppage-time leveler followed by a perfect penalty shootout to get past their arch-rivals in the Gulf and secure a record-extending fourth consecutive Trophee des Champions victory.
The Champions League holders seemed to be coasting towards a comfortable win in the showdown featuring the French league champions and the Coupe de France winners after Ousmane Dembele opened the scoring in the opening stages.
However, the southern French side fired twice late to seize a shock lead. First, Mason Greenwood scored from the penalty spot, before the defender inadvertently turned the ball into his own net for an own goal.
In a breathtaking turn of events, Goncalo Ramos snatched a crucial leveler in the dying moments to send the match into a deciding shootout. PSG goalkeeper Chevalier then emerged as the hero, saving decisive kicks from Matt O'Riley and Traore.
In the shootout, Goncalo Ramos, the midfielder, Nuno Mendes, and the young talent all scored with composure for PSG to complete a convincing penalty win.
Now 14-time champions Paris Saint-Germain, who faced last season's Ligue 1 second-placed team Marseille after achieving a domestic double, have now won this trophy for the twelfth time in the past 13 years.
