PSG has now claimed the season-opening trophy on 14 separate occasions.
Paris Saint-Germain needed a stoppage-time leveler followed by a successful penalty shootout to overcome their arch-rivals in Kuwait and capture a fourth straight French Super Cup title.
The Champions League holders seemed to be coasting towards a comfortable triumph in the match between the French league winners and the French Cup holders after the French winger opened the net early on.
However, the southern French side fired two times late to take a shock lead. First, the English forward scored from the spot-kick, before the defender inadvertently turned the ball into his own net for an own goal.
In a breathtaking twist of fortune, the Portuguese striker grabbed a crucial equaliser in the final moments to send the match into a penalty shootout. PSG goalkeeper Chevalier then stood as the key figure, stopping decisive attempts from Matt O'Riley and Hamed Traore.
From the spot, Goncalo Ramos, the midfielder, the full-back, and the young talent all scored with composure for Paris Saint-Germain to seal a 4-1 shootout victory.
The record winners PSG, who met last season's Ligue 1 runners-up Marseille after achieving a domestic double, have now lifted this trophy for the 12th time in the last 13 years.
