The Parisian club has now secured the season-opening trophy on fourteen different occasions.
The Parisian giants required a dramatic equaliser followed by a perfect penalty shootout to get past their arch-rivals in Kuwait and capture a record-extending fourth consecutive French Super Cup title.
The European champions seemed to be coasting towards a comfortable triumph in the showdown featuring the Ligue 1 winners and the Coupe de France holders after the French winger opened the scoring in the opening stages.
Yet, the southern French side struck twice late to take a shock advantage. First, Mason Greenwood converted from the spot-kick, before Willian Pacho unfortunately directed the ball into his own net for an own-goal.
In a remarkable turn of events, Goncalo Ramos snatched a crucial leveler in the final seconds to force the match into a deciding shootout. The Parisian shot-stopper Chevalier then emerged as the hero, stopping decisive attempts from Matt O'Riley and Traore.
From the spot, Ramos, the midfielder, the full-back, and Desire Doue all converted with composure for PSG to complete a convincing shootout win.
The record champions PSG, who met last season's Ligue 1 runners-up Olympique de Marseille after achieving a domestic double, have now lifted this trophy for the twelfth time in the last 13 years.