PSG has now won the season-opening trophy on 14 different times.
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 seemed to be coasting towards a comfortable win in the showdown featuring the French league champions and the French Cup winners after the French winger opened the net early on.
Yet, the southern French side fired twice in the closing moments to take a surprise lead. First, the English forward converted from the penalty spot, before Willian Pacho unfortunately directed the ball into his own net for an own goal.
In a breathtaking turn of fortune, the Portuguese striker snatched a vital leveler in the final seconds to force the contest into a deciding shootout. PSG goalkeeper Chevalier then stood as the key figure, stopping decisive attempts from Matt O'Riley and Hamed Traore.
In the shootout, Goncalo Ramos, Vitinha, Nuno Mendes, and Desire Doue all converted with composure for PSG to complete a convincing shootout win.
The record winners Paris Saint-Germain, who met last season's Ligue 1 runners-up Marseille after achieving a domestic double, have now won this competition for the twelfth time in the last thirteen years.
