Di Maria's eighth-minute lob put the holders ahead, before adding his second before the half-hour mark, with Thomas Meunier sweeping in a late third.
Thomas Tuchel's men remain on course for a historic treble, as they also lead Ligue 1 by 17 points with a game in hand and will take a 2-0 advantage over Manchester United into the second leg of their Champions League last-16 tie next week.
Head coach Tuchel, with Neymar and Edinson Cavani still out injured ahead of the Man United game, decided to leave Kylian Mbappe on the bench against a Dijon side languishing in the Ligue 1 relegation zone.
The hosts got off to a quick start, with former Stoke City forward Eric Maxim Choupo-Moting denied only his second goal for the club by Dijon goalkeeper Runar Alex Runarsson.
But PSG did not have to wait long to break the deadlock, as Julian Draxler found Di Maria in space, with the Argentinian making the most of poor positioning by Runarsson to loft the ball into the far corner for his 12th goal of the season.
The former Real Madrid winger made it two in the 28th minute, tapping into an empty net after seeing his attempted square pass to Choupo-Moting cut out.
Dijon came agonisingly close to pulling a goal back shortly afterwards, as Julio Tavares rounded home goalkeeper Gianluigi Buffon before his effort from the tightest of angles span out off the inside of the far post.
PSG continued to dominate in the second half with Draxler and Di Maria both going close, but it was full-back Meunier who slotted in Choupo-Moting's cutback to extend the lead with 13 minutes remaining.
On Wednesday, Lyon take on Caen as they look for a first major trophy since winning the French Cup in 2012, while Rennes, buoyed by their run to the Europa League last 16, host Orleans.
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