PSG has now claimed the season-opening cup on 14 different occasions.
The Parisian giants required a stoppage-time leveler followed by a successful spot-kick decider to get past their arch-rivals in Kuwait and secure a fourth straight Trophee des Champions title.
The European champions seemed to be coasting towards a straightforward triumph in the match featuring the Ligue 1 champions and the French Cup winners after the French winger found the net early on.
However, the southern French side struck two times in the closing moments to take a shock lead. Initially, the English forward converted from the spot-kick, before the defender inadvertently directed the ball into his own net for an own-goal.
In a remarkable turn of events, the Portuguese striker snatched a vital leveler in the dying moments to send the match into a penalty shootout. The Parisian shot-stopper Chevalier then stood as the hero, saving decisive kicks from Matt O'Riley and Hamed Traore.
In the shootout, Goncalo Ramos, Vitinha, Nuno Mendes, and Desire Doue all scored with composure for PSG to complete a convincing shootout victory.
The record champions PSG, who faced last season's Ligue 1 second-placed team Olympique de Marseille after completing a domestic double, have now won this trophy for the 12th time in the last 13 seasons.
