The French Ligue 1 champions travelled to Old Trafford missing nearly 400 million euros worth of talent following injuries to defender Thomas Meunier and strikers Neymar and Edinson Cavani.
However a dazzling display from the former United player Angel di Maria and World Cup winner Kylian Mbappé inflicted a first defeat on the United caretaker manager Ole Gunnar Solskjaer.
The 45-year-old Norwegian took over from Jose Mourinho in December and had orchestrated a sequence of 10 wins and a draw.
But the former United striker admitted his side were shown how much they still have to improve following second-half goals from Presnel Kimpembe and Mbappé.
"We weren't at the level," Solskjaer conceded. "This is a level up from what we have played against. We have had a great run. We came into this game in a great frame of mind, great form, but it's a big step up."
In the second leg in Paris on 6 March, United will be without the services of key midfielder Paul Pogba who was dismissed in the closing stages for a second bookable offence.
They might also be without Jesse Lindgard and Anthony Marial who were injured during a game in which Thomas Tuchel's men displayed a collective spirit rarely associated with the side.
Di Maria was the embodiment of defiance. Booed by sections of the crowd for his apparent listlessness during his time at Old Trafford, the Argentine set up both goals and kept his composure. When a beer bottle was thrown at him, he picked it up and pretended to drink from it.
Tuchel was impressed. "I think the guy is very competitive, like all South American guys," said the PSG boss. "If you tease him it does not make him weaker."