PSG has now won the prestigious trophy on fourteen separate times.
Paris Saint-Germain needed a dramatic leveler followed by a perfect spot-kick decider to get past their arch-rivals in the Gulf and secure a fourth straight French Super Cup title.
The Champions League holders appeared to be sailing towards a straightforward win in the showdown between the Ligue 1 winners and the Coupe de France winners after Ousmane Dembele found the net in the opening stages.
However, the southern French side struck two times late to seize a shock lead. First, Mason Greenwood converted from the penalty spot, before Willian Pacho unfortunately directed the ball into his own net for an own-goal.
In a remarkable twist of events, Goncalo Ramos snatched a vital leveler in the dying moments to force the match into a penalty shootout. The Parisian shot-stopper Chevalier then emerged as the key figure, stopping decisive kicks from Matt O'Riley and Hamed Traore.
In the shootout, Ramos, Vitinha, the full-back, and the young talent all converted with composure for PSG to seal a convincing penalty win.
The record winners Paris Saint-Germain, who met last season's Ligue 1 second-placed team Marseille after achieving a league and cup double, have now won this competition for the 12th time in the past thirteen seasons.