PSG has now won the season-opening cup on 14 different times.
The Parisian giants required a dramatic equaliser followed by a perfect spot-kick decider to overcome their arch-rivals in Kuwait and capture a fourth straight Trophee des Champions victory.
The European champions seemed to be coasting towards a comfortable triumph in the showdown featuring the Ligue 1 winners and the Coupe de France winners after the French winger found the net early on.
However, the southern French side struck two times in the closing moments to seize a shock advantage. Initially, the English forward converted from the spot-kick, before Willian Pacho unfortunately directed the ball into his own net for an own-goal.
In a remarkable twist of fortune, the Portuguese striker snatched a vital equaliser in the dying moments to send the contest into a penalty shootout. PSG goalkeeper Chevalier then emerged as the hero, stopping crucial attempts from Matt O'Riley and Traore.
In the shootout, Ramos, Vitinha, the full-back, and the young talent all scored successfully for Paris Saint-Germain to seal a 4-1 penalty victory.
Now 14-time champions PSG, who faced last season's Ligue 1 runners-up Marseille after completing a domestic double, have now lifted this competition for the twelfth time in the last thirteen years.