PSG has now won the prestigious trophy on 14 different occasions.
The Parisian giants required a stoppage-time leveler followed by a perfect 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 appeared to be sailing towards a straightforward triumph in the match between the French league winners and the French Cup holders after the French winger found the scoring early on.
However, Marseille struck two times in the closing moments to seize a shock lead. First, Mason Greenwood converted from the spot-kick, before the defender inadvertently turned the ball into his own net for an own goal.
In a remarkable turn of fortune, the Portuguese striker grabbed a vital leveler in the final seconds to send the match into a deciding shootout. PSG goalkeeper Chevalier then emerged as the key figure, saving crucial kicks from Matt O'Riley and Traore.
From the spot, Goncalo Ramos, Vitinha, Nuno Mendes, and Desire Doue all scored successfully for PSG to complete a convincing penalty victory.
The record winners PSG, who faced last season's Ligue 1 runners-up Marseille after achieving a domestic double, have now won this competition for the 12th time in the past 13 years.
