Di Maria has stepped into the breach since Neymar's metatarsal injury with five goals, the latest two helping seal PSG's progression to the last four with ease.
A sumptuous lob put Thomas Tuchel's side ahead, before he pounced on a loose ball to double their advantage before the break.
Their intensity dropped in the second half but Thomas Meunier added a late third to keep PSG's treble hopes alive.
PSG asserted their dominance early on and, after wasting some early openings, they broke the deadlock after eight minutes, Di Maria producing an audacious first-time lob over Runar Runarsson from Julian Draxler's perfect throughball.
Romain Amalfitano wasted a glorious chance to bring Dijon level, but Di Maria made no mistake when presented with his next opening, the Argentine slamming the ball home after Wesley Lautoa had blocked his initial pass towards Eric Maxim Choupo-Moting.
The visitors had their heads in their hands again in the 32nd minute as Julio Tavares' attempt from a near-impossible angle rolled along the line and flicked the post.
Di Maria should have been celebrating a hat-trick before the break but, after Runarsson had superbly denied Meunier, the forward was thwarted by Fouad Chafik on the line.
Leandro Paredes saw a powerful free-kick tipped over by Runarsson early in the second half, but it was a rare moment of quality as the hosts' level dipped.
Dijon were unable to take advantage, though, with Gianluigi Buffon called into action to push away efforts from Tavares and Amalfitano either side of the hour mark.
Meunier got his goal with 13 minutes to play after good hold-up play from Choupo-Moting, the full-back side-footing past Runarsson to wrap things up.
What does it mean? PSG march on
Beating PSG in this competition must seem impossible for opposition teams, their unbeaten run now stands at 28 matches, stretching all the way back to January 2014. A trophy-laden campaign remains on for Tuchel's men, while Dijon must focus on trying to preserve their Ligue 1 status.
Angel's a Di-light
No Neymar? No problem. Di Maria thrilled throughout at the Parc des Princes and was duly rewarded with two fine goals. The 31-year-old has been involved in 10 goals in his last nine matches in all competitions – six goals and four assists.
Choupo-Moting struggling to fill Cavani gap
Choupo-Moting has now gone 20 games without scoring for PSG in all competitions, a run that stretches back September 23. His problems continued on Tuesday, wasting a glut of chances that would have got his confidence flowing.