The Parisian club has now claimed the prestigious trophy on 14 different times.
Paris Saint-Germain required a stoppage-time leveler followed by a successful spot-kick decider to overcome their arch-rivals in Kuwait and capture a fourth straight Trophee des Champions title.
The Champions League holders seemed to be coasting towards a straightforward triumph in the match between the Ligue 1 winners and the French Cup holders after the French winger found the net early on.
Yet, the southern French side fired twice late to seize a surprise advantage. 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 events, Goncalo Ramos grabbed a crucial leveler in the final seconds to force the contest into a penalty shootout. The Parisian shot-stopper Chevalier then emerged as the hero, saving decisive kicks from Matt O'Riley and Traore.
From the spot, Goncalo Ramos, Vitinha, Nuno Mendes, and Desire Doue all converted successfully for PSG to complete a convincing penalty win.
Now 14-time winners PSG, who faced last season's Ligue 1 second-placed team Marseille after achieving a domestic double, have now won this trophy for the twelfth time in the last thirteen seasons.