PSG has now won the season-opening cup on 14 different occasions.
The Parisian giants required a stoppage-time equaliser followed by a perfect spot-kick decider to get past their arch-rivals in Kuwait and secure a fourth straight French Super Cup victory.
The European champions seemed to be sailing towards a comfortable triumph in the match between the French league winners and the Coupe de France holders after the French winger found the net in the opening stages.
Yet, the southern French side fired two times in the closing moments to take a shock advantage. First, Mason Greenwood converted from the penalty spot, before Willian Pacho inadvertently turned the ball into his own net for an own-goal.
In a breathtaking turn of events, the Portuguese striker snatched a crucial equaliser in the dying seconds to send the contest into a deciding shootout. The Parisian shot-stopper Chevalier then emerged as the hero, saving decisive kicks from Matt O'Riley and Hamed Traore.
In the shootout, Goncalo Ramos, the midfielder, Nuno Mendes, and the young talent all scored with composure for Paris Saint-Germain to complete a 4-1 shootout victory.
The record winners PSG, who met last season's Ligue 1 second-placed team Marseille after achieving a league and cup double, have now lifted this competition for the 12th time in the past 13 seasons.
