PSG has now secured the season-opening cup on 14 different times.
The Parisian giants needed a stoppage-time leveler followed by a perfect spot-kick decider to overcome Marseille in Kuwait and secure a fourth straight French Super Cup title.
The Champions League holders seemed to be coasting towards a straightforward triumph in the match featuring the Ligue 1 winners and the French Cup winners after the French winger found the scoring in the opening stages.
Yet, the southern French side fired twice late to seize a surprise lead. First, the English forward scored from the spot-kick, before Willian Pacho unfortunately turned the ball into his own net for an own-goal.
In a remarkable turn of fortune, the Portuguese striker snatched a vital equaliser in the dying seconds to send the contest into a deciding shootout. The Parisian shot-stopper Chevalier then stood as the hero, stopping decisive attempts from Matt O'Riley and Traore.
From the spot, Goncalo Ramos, the midfielder, the full-back, and the young talent all scored successfully for PSG to seal a convincing shootout victory.
The record winners PSG, who met last season's Ligue 1 runners-up Marseille after completing a league and cup double, have now lifted this competition for the 12th time in the past 13 seasons.