PSG has now won the season-opening trophy on 14 different occasions.
The Parisian giants needed a stoppage-time equaliser followed by a perfect spot-kick decider to overcome their arch-rivals in the Gulf and capture a record-extending fourth consecutive French Super Cup victory.
The Champions League holders appeared to be coasting towards a comfortable win in the match between the French league winners and the French Cup winners after the French winger opened the net early on.
However, the southern French side struck twice late to take a surprise advantage. First, Mason Greenwood scored from the penalty spot, before Willian Pacho unfortunately directed the ball into his own net for an own goal.
In a breathtaking twist of events, Goncalo Ramos snatched a crucial equaliser in the dying seconds to force the contest into a deciding shootout. The Parisian shot-stopper Chevalier then emerged as the hero, saving crucial kicks from Matt O'Riley and Hamed Traore.
In the shootout, Goncalo Ramos, Vitinha, Nuno Mendes, and Desire Doue all converted with composure for Paris Saint-Germain to seal a 4-1 shootout win.
The record champions PSG, who faced last season's Ligue 1 runners-up Olympique de Marseille after achieving a domestic double, have now won this competition for the 12th time in the past thirteen years.
