PSG has now secured the season-opening trophy on 14 separate times.
Paris Saint-Germain required a dramatic leveler followed by a perfect spot-kick decider to get past their arch-rivals in Kuwait and capture a fourth straight French Super Cup victory.
The Champions League holders appeared to be sailing towards a straightforward triumph in the match featuring the Ligue 1 champions and the French Cup winners after the French winger found the scoring early on.
Yet, the southern French side struck twice late to take a surprise lead. First, the English forward 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 force the match into a penalty shootout. PSG goalkeeper Chevalier then emerged as the key figure, saving crucial kicks from Matt O'Riley and Traore.
In the shootout, Goncalo Ramos, the midfielder, Nuno Mendes, and the young talent all converted with composure for PSG to seal a convincing penalty win.
The record winners Paris Saint-Germain, who met last season's Ligue 1 second-placed team Marseille after completing a league and cup double, have now lifted this trophy for the twelfth time in the past 13 seasons.
