PSG has now secured the season-opening cup on 14 separate occasions.
The Parisian giants required a stoppage-time leveler followed by a successful spot-kick decider to overcome Marseille in Kuwait and capture a record-extending fourth consecutive French Super Cup title.
The European champions appeared to be coasting towards a comfortable triumph in the showdown featuring the French league winners and the French Cup holders after the French winger opened the scoring early on.
Yet, the southern French side struck two times late to take a surprise lead. Initially, the English forward converted from the penalty spot, before the defender unfortunately turned the ball into his own net for an own goal.
In a breathtaking turn of events, the Portuguese striker snatched a crucial leveler in the dying moments to force the match into a deciding shootout. The Parisian shot-stopper Chevalier then emerged as the hero, saving decisive attempts from Matt O'Riley and Traore.
From the spot, Ramos, Vitinha, the full-back, and Desire Doue all converted successfully for PSG to seal a convincing penalty victory.
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 competition for the twelfth time in the past thirteen seasons.