PSG host relegation battling Le Havre on Saturday
Skipper Antonio Valencia and Lingard punished woeful Arsenal defending to put United two ahead inside 11 minutes at the Emirates and Lingard struck again in the 63rd minute after Alexandre Lacazette's goal had revived home hopes.
Keeper David De Gea was inspired for United who had to play the final 15 minutes with 10 men after record signing Paul Pogba was shown a straight red card for a reckless 'studs up' foul on Arsenal right back Hector Bellerin.
United's first away victory over a 'top-six' rival since Jose Mourinho took charge meant they cut Manchester City's lead to five points, although Pep Guardiola's side host struggling West Ham United on Sunday.