The Parisian club has now secured the season-opening cup on 14 different times.
Paris Saint-Germain needed a stoppage-time leveler followed by a perfect spot-kick decider to get past Marseille in Kuwait and secure a fourth straight French Super Cup victory.
The Champions League holders seemed to be coasting towards a straightforward win in the match between the Ligue 1 champions and the French Cup holders after the French winger found the net in the opening stages.
Yet, the southern French side fired two times in the closing moments to seize a shock lead. First, the English forward scored from the penalty spot, before Willian Pacho unfortunately turned the ball into his own net for an own goal.
In a remarkable turn of events, Goncalo Ramos snatched a vital equaliser in the final moments to force the match into a penalty shootout. The Parisian shot-stopper Lucas Chevalier then emerged as the key figure, stopping crucial kicks from Matt O'Riley and Traore.
From the spot, Ramos, the midfielder, Nuno Mendes, and the young talent all converted successfully for PSG to complete a 4-1 shootout victory.
Now 14-time champions PSG, who faced last season's Ligue 1 runners-up Olympique de Marseille after achieving a league and cup double, have now won this competition for the 12th time in the last 13 seasons.