The Parisian club has now won the prestigious cup on 14 different times.
Paris Saint-Germain needed a dramatic equaliser followed by a successful spot-kick decider to get past their arch-rivals in Kuwait and secure a record-extending fourth consecutive Trophee des Champions title.
The Champions League holders appeared to be coasting towards a comfortable win in the match between the Ligue 1 champions and the French Cup winners after Ousmane Dembele opened the net early on.
However, the southern French side fired twice late to seize a surprise lead. Initially, Mason Greenwood scored from the penalty spot, before Willian Pacho unfortunately directed the ball into his own net for an own goal.
In a breathtaking twist of fortune, the Portuguese striker grabbed a crucial equaliser in the final moments to send the contest into a penalty shootout. PSG goalkeeper Chevalier then stood as the hero, stopping crucial kicks from Matt O'Riley and Traore.
From the spot, Goncalo Ramos, the midfielder, the full-back, and the young talent all scored successfully for Paris Saint-Germain to complete a 4-1 penalty victory.
The record champions Paris Saint-Germain, who met last season's Ligue 1 second-placed team Olympique de Marseille after completing a domestic double, have now won this competition for the 12th time in the past thirteen years.