The Parisian club has now won the season-opening trophy on 14 different times.
The Parisian giants required a stoppage-time equaliser followed by a perfect spot-kick decider to overcome their arch-rivals in the Gulf and capture a fourth straight Trophee des Champions victory.
The European champions appeared to be coasting towards a comfortable triumph in the match between the Ligue 1 champions and the Coupe de France winners after Ousmane Dembele opened the net in the opening stages.
However, the southern French side fired twice late to seize a surprise lead. First, the English forward 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, the Portuguese striker snatched a crucial leveler in the final seconds to force the contest into a deciding shootout. The Parisian shot-stopper Chevalier then emerged as the key figure, saving crucial attempts from Matt O'Riley and Hamed Traore.
From the spot, Ramos, the midfielder, the full-back, and Desire Doue all converted successfully for PSG to complete a convincing shootout victory.
The record winners Paris Saint-Germain, who faced last season's Ligue 1 runners-up Marseille after achieving a domestic double, have now lifted this trophy for the 12th time in the past 13 years.