PSG were without their potent three-pronged attack of Edinson Cavani, Neymar and Kylian Mbappe, but the league leaders' makeshift side made light work of the contest and could have won by a much bigger margin.
Dijon's Icelandic keeper Runar Runarsson made a string of superb saves in the first half but could do nothing about Di Maria's brace, with both goals created in sublime fashion by German playmaker Julian Draxler.
Di Maria opened the scoring in the eighth minute with a brilliant lob from the edge of the penalty area after a defence-splitting pass by Draxler, who also set up the second with what was almost a carbon copy of his earlier assist.
Di Maria showed a different kind of composure this time, with his mistimed pass to Eric Choupo-Moting rebounding kindly to the Argentina winger who swept the ball home past the stranded Runarsson.
Dijon defender Fouad Chafik denied Di Maria a first-half hat-trick as he cleared the livewire forward's shot off the line while Julio Tavares hit the post at the other end after a rare Dijon break.
The busy Runarsson twice kept out superb Draxler chances before Choupo-Moting, who missed three good opportunities, set up Meunier with some fine footwork and the Belgium midfielder responded with a clever 76th-minute finish to put the icing on the cake.
In the other quarter-finals, Rennes are at home to second division Orleans and Olympique Lyonnais take on Caen on Wednesday, while fourth division Vitre are at home to Nantes on March 6.
(Writing by Zoran Milosavljevic; Editing by Toby Davis)
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