The Parisian club has now won the season-opening trophy on fourteen separate times.
The Parisian giants required a stoppage-time equaliser followed by a perfect spot-kick decider to get past their arch-rivals in Kuwait and capture a record-extending fourth consecutive French Super Cup victory.
The European champions seemed to be coasting towards a comfortable triumph in the showdown between the Ligue 1 winners and the Coupe de France winners after the French winger opened the scoring 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 remarkable turn of events, Goncalo Ramos snatched a vital leveler in the final moments to send the contest into a deciding shootout. PSG goalkeeper Chevalier then emerged as the key figure, saving crucial kicks from Matt O'Riley and Hamed Traore.
In the shootout, Ramos, Vitinha, Nuno Mendes, and Desire Doue all scored with composure for Paris Saint-Germain to seal a convincing 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 won this competition for the 12th time in the past thirteen seasons.
