PSG has now secured the season-opening trophy on 14 different occasions.
The Parisian giants required a stoppage-time equaliser followed by a successful spot-kick decider to overcome their arch-rivals in Kuwait and capture a fourth straight French Super Cup victory.
The Champions League holders appeared to be sailing towards a comfortable win in the showdown between the Ligue 1 champions and the Coupe de France winners after the French winger found the scoring in the opening stages.
Yet, the southern French side fired twice in the closing moments to take a shock advantage. First, Mason Greenwood scored from the penalty spot, before the defender unfortunately directed the ball into his own net for an own-goal.
In a remarkable turn of events, Goncalo Ramos grabbed a vital equaliser in the final seconds to send the contest into a penalty shootout. PSG goalkeeper Chevalier then emerged as the key figure, saving decisive kicks from Matt O'Riley and Traore.
In the shootout, Ramos, the midfielder, the full-back, and Desire Doue all scored successfully for PSG to complete a convincing penalty win.
The record winners Paris Saint-Germain, who met last season's Ligue 1 second-placed team Olympique de Marseille after achieving a league and cup double, have now lifted this competition for the 12th time in the last 13 years.
