PSG has now won the prestigious cup on fourteen different occasions.
Paris Saint-Germain needed a dramatic equaliser followed by a successful spot-kick decider to get past their arch-rivals in Kuwait and capture a fourth straight French Super Cup title.
The European champions appeared to be coasting towards a straightforward win in the showdown featuring the French league winners and the French Cup holders after the French winger found the net early on.
However, the southern French side struck two times late to seize a shock lead. First, Mason Greenwood scored from the penalty spot, before Willian Pacho inadvertently directed the ball into his own net for an own-goal.
In a remarkable turn of fortune, the Portuguese striker grabbed a crucial equaliser in the final moments to force the match into a deciding shootout. The Parisian shot-stopper Chevalier then stood as the hero, stopping decisive kicks from Matt O'Riley and Traore.
In the shootout, Ramos, Vitinha, the full-back, and the young talent all scored with composure for PSG to complete a 4-1 penalty win.
The record champions Paris Saint-Germain, who met last season's Ligue 1 runners-up Olympique de Marseille after achieving a league and cup double, have now lifted this trophy for the twelfth time in the past thirteen seasons.
