The Parisian club has now won the season-opening trophy on 14 separate times.
Paris Saint-Germain needed a dramatic equaliser followed by a perfect penalty shootout to get past their arch-rivals in the Gulf and capture a fourth straight French Super Cup victory.
The European champions appeared to be sailing towards a straightforward win in the match between the Ligue 1 winners and the Coupe de France winners after the French winger opened the net early on.
However, the southern French side struck twice late to seize a surprise lead. Initially, the English forward converted from the spot-kick, before Willian Pacho inadvertently turned the ball into his own net for an own goal.
In a breathtaking turn of events, Goncalo Ramos snatched a vital equaliser in the dying seconds to send the match into a deciding shootout. PSG goalkeeper Lucas Chevalier then emerged as the key figure, saving crucial attempts from Matt O'Riley and Traore.
From the spot, Ramos, the midfielder, the full-back, and the young talent all scored successfully for PSG to complete a convincing penalty victory.
Now 14-time winners Paris Saint-Germain, who met last season's Ligue 1 second-placed team Marseille after achieving a league and cup double, have now lifted this trophy for the twelfth time in the last 13 seasons.