PSG has now secured the prestigious trophy on fourteen different occasions.
The Parisian giants required a stoppage-time equaliser followed by a successful spot-kick decider to get past their arch-rivals in Kuwait and secure a record-extending fourth consecutive French Super Cup victory.
The European champions appeared to be coasting towards a straightforward triumph in the match between the Ligue 1 winners and the French Cup holders after Ousmane Dembele found the net 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 Willian Pacho inadvertently turned the ball into his own net for an own-goal.
In a breathtaking twist of fortune, the Portuguese striker snatched a crucial leveler in the dying moments to force the match into a penalty shootout. The Parisian shot-stopper Chevalier then stood as the hero, saving crucial attempts from Matt O'Riley and Hamed Traore.
From the spot, Goncalo Ramos, the midfielder, the full-back, and Desire Doue all converted with composure for PSG to complete a convincing penalty win.
Now 14-time winners Paris Saint-Germain, who faced last season's Ligue 1 second-placed team Marseille after completing a league and cup double, have now won this competition for the 12th time in the last 13 seasons.