One not unlike the goal he scored for Argentina at the 2018 World Cup.
Gareth Bale also had a goal ruled out by VAR, with the loss putting further pressure on Zinedine Zidane, whose win ratio has been below 50 per cent since his return to the Bernabeu in March 2019.
Mauro Icardi made his first start for the home side after his arrival on loan from Inter, but his fellow countryman Di Maria stole the show.
PSG, confusingly wearing white while the visitors wore dark blue, opened the scoring in the 14th minute when Di Maria latched onto a Juan Bernat cutback from the left byline and fired in, although Courtois should have done better.
Gareth Bale has quickly gone from outcast to offensive workhorse with the way the season has started.
Former Everton midfielder Idrissa Gueye was heavily involved, charging forward with the ball by the touchline before he found his team-mate in space.
They didn't hold back in their assessment of the 28-year-old Belgium ace, handing him a 2/10 rating.
Neymar and Mbappe were sitting next to each other in the stand and could not contain their delight, but it was nearly quickly diminished two minutes later in the 35th minute.
"I'm very happy with the whole team because it was really hard, we had a lot of chances, but there were also some stages for Real where we suffered", Tuchel told RMC Sport.
Di Maria's first-half double was added to late on by Thomas Meunier to complete the rout but in truth, the game had been over as a contest long before Anthony Taylor blew his whistle for the last time into the Paris night sky.
Madrid were also handicapped by the absences of Sergio Ramos, Nacho and Marcelo in defence as well as Ballon d'Or victor Luka Modric from their midfield.