PSG has now won the prestigious trophy on 14 separate occasions.
Paris Saint-Germain needed a dramatic leveler followed by a perfect spot-kick decider to get past their arch-rivals in Kuwait and capture a fourth straight Trophee des Champions victory.
The European champions appeared to be sailing towards a comfortable win in the showdown between the Ligue 1 champions and the Coupe de France winners after the French winger opened the net in the opening stages.
Yet, the southern French side fired two times in the closing moments to seize a shock advantage. First, the English forward converted from the penalty spot, before the defender inadvertently turned the ball into his own net for an own goal.
In a breathtaking turn of fortune, Goncalo Ramos snatched a vital leveler in the dying moments to force the match into a penalty shootout. The Parisian shot-stopper Chevalier then stood as the hero, saving decisive attempts from Matt O'Riley and Traore.
In the shootout, Ramos, the midfielder, the full-back, and Desire Doue all scored with composure for PSG to complete a convincing shootout victory.
Now 14-time winners PSG, who faced last season's Ligue 1 runners-up Olympique de Marseille after completing a domestic double, have now won this competition for the 12th time in the last 13 seasons.