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 Wednesday, 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 were 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 were rewarded for their 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 their 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 hosts against the shot-shy 13-time champions of Europe.
What does it mean? PSG in pole position
With Club Brugge and Galatasaray – who played out a 0-0 draw earlier on Wednesday – the other teams in Group A, PSG and Madrid have been tipped to battle it out for top spot. Victory over Los Blancos in Paris handed Tuchel's team the advantage, and when they visit the Santiago Bernabeu in November they should prove even more dangerous opponents with Neymar, Mbappe and Cavani likely to be available for selection.
Formidable Gueye dictates the play
Gueye was everywhere for PSG, dominating the midfield in a way that offered Marco Verratti more creative license. The Senegal international showed great energy to maintain the high press and stifle Madrid, while also adding an assist for Di Maria's second goal.
Militao missing at key moments
When Bernat burst down the left to set up the opener, Militao made no move to get across and put Di Maria under pressure. The Brazil international then allowed Di Maria to peel off him far too easily before he drilled in the second.
PSG face a tricky trip to Lyon in Ligue 1 on Sunday, with Madrid visiting LaLiga leaders Sevilla on the same day.