PSG has now secured the season-opening trophy on fourteen different occasions.
The Parisian giants needed a dramatic leveler followed by a successful spot-kick decider to overcome their arch-rivals in Kuwait and capture a fourth straight French Super Cup victory.
The Champions League holders appeared to be coasting towards a comfortable win in the match featuring the French league champions and the Coupe de France winners after Ousmane Dembele found the net in the opening stages.
However, the southern French side fired two times in the closing moments 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 breathtaking turn of fortune, the Portuguese striker snatched a vital equaliser in the final seconds to send the contest into a penalty shootout. The Parisian shot-stopper Chevalier then emerged as the hero, saving decisive kicks from Matt O'Riley and Traore.
From the spot, Ramos, the midfielder, the full-back, and the young talent all converted with composure for Paris Saint-Germain to complete a 4-1 shootout victory.
Now 14-time winners PSG, who met last season's Ligue 1 second-placed team Olympique de Marseille after achieving a domestic double, have now won this competition for the 12th time in the last 13 years.