PSG has now won the season-opening trophy on 14 different occasions.
The Parisian giants needed a stoppage-time leveler followed by a perfect spot-kick decider to get past their arch-rivals in the Gulf and secure a fourth straight French Super Cup title.
The Champions League holders appeared to be coasting towards a straightforward win in the showdown between the Ligue 1 champions and the French Cup winners after the French winger opened the net in the opening stages.
However, Marseille fired twice late 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 breathtaking twist of events, the Portuguese striker grabbed a crucial leveler in the dying seconds to send the contest into a deciding shootout. The Parisian shot-stopper Chevalier then emerged as the hero, saving 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 PSG to seal a 4-1 penalty victory.
The record champions PSG, who met last season's Ligue 1 runners-up Olympique de Marseille after completing a domestic double, have now lifted this trophy for the twelfth time in the past 13 seasons.
