PSG has now won the season-opening trophy on 14 separate times.
The Parisian giants required a dramatic equaliser followed by a successful spot-kick decider to overcome Marseille in Kuwait and capture a record-extending fourth consecutive French Super Cup victory.
The Champions League holders appeared to be coasting towards a straightforward win in the match featuring the Ligue 1 winners and the French Cup winners after the French winger found the scoring early on.
However, the southern French side struck two times late to seize a shock lead. First, the English forward converted from the spot-kick, before Willian Pacho inadvertently directed the ball into his own net for an own-goal.
In a remarkable turn of fortune, the Portuguese striker grabbed a crucial leveler in the final moments to send the contest into a deciding shootout. The Parisian shot-stopper Chevalier then stood as the key figure, saving decisive attempts from Matt O'Riley and Hamed Traore.
In the shootout, Goncalo Ramos, Vitinha, Nuno Mendes, and the young talent all scored successfully for PSG to complete a 4-1 penalty victory.
Now 14-time champions PSG, who met last season's Ligue 1 second-placed team Marseille after achieving a domestic double, have now won this competition for the 12th time in the last thirteen years.