Thomas Tuchel was unable to pick the suspended Neymar or injured duo Kylian Mbappe and Edinson Cavani for the Group A clash at the Parc des Princes on Thursday (AEST), but Di Maria played a starring role against his former club.
Despite having Eden Hazard, Karim Benzema and Gareth Bale on the field together for the first time, Madrid lacked sharpness and was put to the sword by the Argentina international twice inside 33 minutes.
Bale had what would have been a spectacular goal ruled out for handball after a VAR review and Zinedine Zidane's side were punished for failing to register a single shot on target when Thomas Meunier compounded their misery at the culmination of a stoppage-time counter-attack.
Pablo Sarabia appealed for a penalty when he kicked the ball against the arm of Eder Militao – making his first Madrid start with Sergio Ramos suspended – in the first minute, but on that occasion referee Anthony Taylor was unmoved.
PSG was rewarded for its vibrant start in the 14th minute when Mauro Icardi, handed a full debut after his deadline-day loan move from Inter, combined with Juan Bernat, who squared for Di Maria to stab past Thibaut Courtois at his near post.
After Hazard and Bale fired narrowly off target, PSG doubled its lead when Idrissa Gueye teed up Di Maria and the ex-Madrid winger fired a stunning drive home from the edge of the box.
Bale thought he had halved the deficit two minutes later when he lobbed former team-mate Keylor Navas, only for a VAR intervention to reveal the ball touched his arm while he juggled it before shooting.
Di Maria scooped a chance to complete his hat-trick over before Eric Maxim Choupo-Moting replaced Icardi in the 60th minute, while Courtois did well to keep out Sarabia.
After PSG lost Marquinhos to injury, Benzema had a goal ruled out for offside and headed narrowly wide with 12 minutes remaining.
Madrid crumbled in the 91st minute when full-backs Meunier and Bernat surged forward and the Belgian slotted home to round off an impressive win for the host against the shot-shy 13-time champion of Europe.