PSG were without Neymar, Kylian Mbappe and Edinson Cavani but still managed to put three past the 13-time European champions.
It looked like Real were back in the game in the 35th minute when Gareth Bale lobbed Keylor Navas to make it 2-1, only for VAR to determine there was a handball in the build-up.
On the whole it was a massively disappointing night for Zinedine Zidane's side, who continue to show how much they miss Cristiano Ronaldo.
Bale, Karim Benzema and £90m signing Eden Hazard all featured in a star-studded attacking line-up yet were unable to make a real impact.
Hazard - who only recently returned from injury - was particularly poor and only lasted 70 minutes, leaving the pitch for Lucas Vazquez.
Fellow former Chelsea player Thibaut Courtois also had a game to forget as he gifted PSG a 14th-minute lead and once again failed to record a clean sheet.
Not since February has the Belgian goalkeeper managed to keep out the opposition for Los Blancos.
Hazard and Courtois inevitably received low ratings from the media for their performances and they'll want to avoid reading all reviews from the Spanish press today.
Courtois: "Whatever gets thrown at him, Courtois can't seem to save it. He didn't commit any glaring errors but had a night to forget in Paris. The Belgian let the first goal in at his near post and couldn't do much else to prevent a second and a third. All while Keylor Navas watched from the other end."
Hazard: "Real Madrid's Galactico signing didn't hide but he didn't have an impact on the game either. They need him to be at his best sooner rather than later."
Courtois: "Terrible mistake on Di Maria's opening goal, leaving his near post exposed and unable to get a hand on the ball despite it being close enough to him. Slow on the second goal too. He did make the occasional decent save at the start of the second half when PSG were piling on the pressure, but overall looked indecisive."
Hazard: "Trapped on the left, when he had the ball he showed touches of quality but was unable to make a decisive impact. He came off for Lucas at the same time as James. He still looks somewhat out of shape, which is devastating for his game."
Courtois: "Fallon. The Belgian could have done more for Di Maria's opener and was lucky that PSG missed clear chances."
Hazard: "Innocuous. He appeared little in the game and wasn't the decisive player that everyone expects at Real Madrid."News Now - Sport News