Luciano Narsingh and Hector Moreno found the net as the Dutch champions recorded a narrow triumph over United on their first Champions League match in 17 months.
But Moreno should have not been on the pitch to head PSV level after Memphis Depay’s opener.
With 15 minutes gone, the Mexican slid in with a late two-footed challenge on Shaw in the box.
The England defender was carried off on a stretcher while receiving oxygen eight minutes later.
Disturbing replays showed Shaw’s right foot bent at a 45-degree angle.
Incredibly, referee Nicola Rizzoli did not award a penalty and Moreno was allowed to equalise Depay’s stunning solo opener with a header.
Then, just before the hour, Narsingh took advantage of some slack marking from Shaw’s replacement Marcos Rojo to finish off a counter and give the hosts an historic win that gives them an early advantage in Group B.
Shaw later took to Twitter, as many well-wishers sent him notes of support.
He wrote: “Thank you everyone for your messages , words can’t describe how gutted I am , my road to recovery starts now, I will come back stronger.” His former club Southampton told Shaw to “come back stronger”, to which he replied: “thank you , you don’t know how much you as a club mean to me , thank you so much”.
United confirmed the injury as a double fracture of the right leg.
Defender Chris Smalling wished team-mate Shaw a speedy recovery.
He said: “I didn’t see it first hand but I know that a few of the players did witness it. It’s a very sad time and we wish him a quick recovery.”
United manager manager Louis van Gaal said: “It is awful. The boy is in his second season and he has been playing fantastic. And now this happens.
“He had the oxygen mask on and was crying in the dressing room. You must judge for yourself. If I say it was a penalty and a red card then I am a bad loser.
“It was a very bad tackle.”
Even though Anthony Martial impressed on his full debut, Van Gaal will be disappointed that United’s return to Europe’s biggest club competition ended in a loss.
As a former Ajax coach and player, Van Gaal would have expected a hostile reception at the Philips Stadion.
Before the first whistle, it was clear the United manager and his team would not be made welcome by the supporters of Ajax’s great rivals.
Van Gaal’s name and that of former Ajax player Daley Blind were booed loudly when they were read out on the public address system.
The atmosphere turned flat in the 15th minute, however, when Shaw was sent flying into the air and dumped on to the turf by Moreno’s challenge.
The left-back ran into the box at full pace only to be chopped down by Moreno from behind. He lay in agony on the floor with his right foot at an angle.
After lengthy treatment, Shaw was carried off on a stretcher and driven to hospital. It subsequently transpired that he had suffered a double leg fracture and was later transfered to Manchester where he will be operated on.
With such a subdued atmosphere, the game struggled to spark into life.
Martial headed a free-kick wide, but, despite lots of possession, United lacked a killer touch.
Thankfully for Van Gaal, Depay was in the mood to show his former employers what they were missing. The Dutchman received a pass from Blind, skipped past Santiago Arias and Jeffrey Bruma before slotting the ball through the legs of PSV goalkeeper Jeroen Zoet.
As he had promised, Depay celebrated, but not wildly.
Any celebrations were short-lived, however, as PSV equalised five minutes later. Moreno shrugged off Matteo Darmian to head in Maxime Lestienne’s corner. Blind tried to clear but instead ended up helping the ball in with his head.
The game turned full circle as PSV took the lead after half-time. Lestienne was the provider again. He latched on to a crisp volleyed pass from Andres Guardado and floated a ball over Rojo’s head for Narsingh, who nodded in.
United had a chance to reply soon after when Bastian Schweinsteiger chipped into the box, but Juan Mata mis-controlled with the goal gaping.
Luuk de Jong missed a good chance to score a third, but the PSV fans were happy to settle for a 2-1 win.
“It’s the same as the game against Swansea,” Van Gaal said. “We are dominating the game, we are creating chances but we are not finishing.
“It’s fantastic for PSV, but for us it’s very bad.”
Zoet, Arias, Bruma, Moreno, Brenet, Narsingh, Propper, Hendrix, Guardado (Schaars 71), Lestienne (Locadia 85), de Jong.
De Gea, Darmian, Smalling, Blind, Shaw (Rojo 24), Schweinsteiger, Ander Herrera (Fellaini 75), Young (Valencia 86), Mata, Depay, Martial.
Nicola Rizzoli (Italy).