The Parisian club has now won the season-opening trophy on 14 separate times.
Paris Saint-Germain required a dramatic equaliser followed by a perfect spot-kick decider to overcome their arch-rivals in the Gulf and capture a fourth straight Trophee des Champions title.
The European champions appeared to be sailing towards a comfortable win in the match featuring the French league champions and the French Cup holders after the French winger opened the scoring early on.
However, the southern French side fired twice in the closing moments to take a surprise lead. Initially, the English forward scored 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, Goncalo Ramos grabbed a crucial leveler in the final seconds to send the contest into a penalty shootout. The Parisian shot-stopper Chevalier then stood as the hero, saving crucial kicks from Matt O'Riley and Traore.
In the shootout, Ramos, the midfielder, the full-back, and the young talent all scored successfully for PSG to seal a convincing shootout victory.
Now 14-time champions Paris Saint-Germain, who met last season's Ligue 1 runners-up Olympique de Marseille after completing a league and cup double, have now won this trophy for the twelfth time in the past thirteen seasons.