PSG has now secured the season-opening trophy on 14 separate occasions.
The Parisian giants needed a stoppage-time equaliser followed by a successful spot-kick decider to get past their arch-rivals in Kuwait and secure a record-extending fourth consecutive French Super Cup victory.
The European champions seemed to be sailing towards a comfortable win in the match between the French league champions and the Coupe de France holders after the French winger found the scoring early on.
Yet, Marseille struck twice in the closing moments to seize a shock lead. First, the English forward converted from the penalty spot, before the defender unfortunately 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 contest into a deciding shootout. The Parisian shot-stopper Chevalier then emerged as the hero, stopping decisive attempts from Matt O'Riley and Traore.
In the shootout, Goncalo Ramos, Vitinha, the full-back, and Desire Doue all converted successfully for PSG to complete a 4-1 shootout win.
Now 14-time winners 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 13 years.
