PSG has now claimed the season-opening trophy on fourteen different times.
Paris Saint-Germain 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 coasting towards a straightforward win in the showdown between the French league champions and the Coupe de France holders after Ousmane Dembele opened the scoring in the opening stages.
However, the southern French side struck two times in the closing moments to take a surprise lead. 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 twist of events, Goncalo Ramos snatched a vital equaliser in the final seconds to force the match into a penalty shootout. PSG goalkeeper Chevalier then emerged as the key figure, stopping crucial attempts from Matt O'Riley and Hamed Traore.
From the spot, Ramos, the midfielder, the full-back, and the young talent all converted successfully for PSG to seal a 4-1 penalty victory.
Now 14-time winners Paris Saint-Germain, who met last season's Ligue 1 second-placed team Marseille after completing a domestic double, have now won this competition for the twelfth time in the past thirteen seasons.