Unai Emery's charges, who are hoping to win the trophy for the fifth year running, were handed a major boost when opposition goalkeeper Regis Gurtner was sent off in the 34th minute for a foul on Kylian Mbappe.
The Brazilian stepped up to the spot and duly sent substitute keeper Jean-Christophe Bouet the wrong way with a well-placed effort, subsequently celebrating his goal by taking off one of his boots and juggling it on his head.
However, Adrien Rabiot succeeded in doubling PSG's lead in the 78th minute by heading in off the post from Di Maria's corner, with VAR judging the effort to have crossed the line.
AMIENS (4-2-3-1): Gurtner; Avelar (Ielsch 12'), Gouano, Adenon, El Hajjam; Fofana, Monconduit; Manzala (Gope-Fenepej 76'), Kakuta, Gakpe; Konate (Bouet 37')
PSG (4-3-3): Trapp; Berchiche, Silva, Marquinhos, Meunier; Draxler (Lo Celso 68'), Rabiot (Alves 80'), Verratti (Nkunku 80'); Neymar, Mbappe, Di Maria