PSG has now won the season-opening cup on 14 different occasions.
Paris Saint-Germain required a stoppage-time leveler followed by a perfect spot-kick decider to overcome their arch-rivals in the Gulf and capture a fourth straight French Super Cup victory.
The Champions League holders appeared to be sailing towards a comfortable triumph in the match featuring the Ligue 1 champions and the Coupe de France winners after Ousmane Dembele found the scoring early on.
However, the southern French side struck two times late to take a shock advantage. First, Mason Greenwood scored from the spot-kick, before the defender unfortunately directed the ball into his own net for an own goal.
In a breathtaking turn of events, Goncalo Ramos grabbed a vital equaliser in the dying seconds to force the contest into a penalty shootout. PSG goalkeeper Lucas Chevalier then emerged as the key figure, saving crucial attempts from Matt O'Riley and Hamed Traore.
From the spot, Ramos, the midfielder, Nuno Mendes, and Desire Doue all converted successfully for Paris Saint-Germain to complete a convincing penalty victory.
The record champions Paris Saint-Germain, who faced last season's Ligue 1 runners-up Olympique de Marseille after completing a league and cup double, have now lifted this competition for the twelfth time in the past 13 seasons.