The Parisian club has now won the season-opening cup on 14 separate times.
Paris Saint-Germain needed a stoppage-time equaliser followed by a perfect spot-kick decider to get past their arch-rivals in the Gulf and secure a fourth straight French Super Cup victory.
The European champions seemed to be coasting towards a comfortable win in the match between the Ligue 1 champions and the Coupe de France winners after the French winger opened the net early on.
However, the southern French side fired twice late to seize a shock advantage. Initially, the English forward converted from the penalty spot, before the defender inadvertently turned the ball into his own net for an own-goal.
In a remarkable turn of fortune, the Portuguese striker grabbed a crucial equaliser in the final seconds to send the match into a penalty shootout. PSG goalkeeper Chevalier then stood as the key figure, stopping decisive attempts from Matt O'Riley and Hamed Traore.
In the shootout, Ramos, Vitinha, Nuno Mendes, and Desire Doue all scored successfully for PSG to complete a 4-1 penalty win.
The record champions PSG, who faced last season's Ligue 1 second-placed team Olympique de Marseille after achieving a domestic double, have now won this trophy for the twelfth time in the last thirteen years.
