PSG has now won the season-opening cup on 14 different times.
Paris Saint-Germain needed a stoppage-time leveler followed by a successful spot-kick decider to get past their arch-rivals in Kuwait and secure a fourth straight French Super Cup victory.
The European champions seemed to be coasting towards a comfortable triumph in the match between the French league winners and the French Cup holders after the French winger found the net in the opening stages.
Yet, Marseille struck two times in the closing moments to seize a surprise lead. Initially, the English forward converted from the spot-kick, before Willian Pacho unfortunately directed the ball into his own net for an own-goal.
In a remarkable turn of fortune, the Portuguese striker snatched a vital equaliser in the dying seconds to send the contest into a deciding shootout. PSG goalkeeper Lucas Chevalier then stood as the hero, saving decisive attempts from Matt O'Riley and Traore.
In the shootout, Goncalo Ramos, the midfielder, Nuno Mendes, and Desire Doue all scored successfully for PSG to seal a 4-1 shootout win.
The record champions Paris Saint-Germain, who faced last season's Ligue 1 runners-up Marseille after achieving a domestic double, have now won this trophy for the 12th time in the past thirteen seasons.
