PSG has now claimed the prestigious cup on fourteen separate times.
The Parisian giants needed a dramatic equaliser followed by a successful spot-kick decider to overcome their arch-rivals in Kuwait and secure a fourth straight French Super Cup title.
The Champions League holders seemed to be coasting towards a straightforward win in the showdown between the Ligue 1 winners and the French Cup holders after the French winger found the net early on.
Yet, the southern French side fired twice in the closing moments to take a surprise advantage. First, the English forward converted from the penalty spot, before the defender inadvertently directed the ball into his own net for an own goal.
In a remarkable twist of fortune, Goncalo Ramos snatched a crucial equaliser in the dying moments to send the contest into a penalty shootout. PSG goalkeeper Chevalier then stood as the hero, saving decisive kicks from Matt O'Riley and Traore.
In the shootout, Goncalo Ramos, the midfielder, the full-back, and the young talent all converted successfully for Paris Saint-Germain to seal a convincing shootout win.
The record champions Paris Saint-Germain, who faced last season's Ligue 1 second-placed team Marseille after completing a domestic double, have now won this competition for the twelfth time in the past thirteen seasons.