Jesse Lingard’s stoppage-time strike denied Burnley a famous win at Old Trafford but he could not stop Manchester United’s fading title hopes from suffering another blow.
Ashley Barnes fired the Clarets ahead after three minutes when Johann Berg Gudmundsson’s free-kick was not cleared, and Steven Defour made it 2-0 with a superb 30-yard free-kick into the top corner.
Lingard came off the bench for the second half and quickly reduced the deficit with a clever back-heel finish from an Ashley Young cross.
United had 75% of possession after the break but struggled to turn their pressure into clear chances until the ball broke to Lingard on the edge of the area in the 91st minute, and he fired into the bottom corner.
It was a dramatic end to a thrilling game but still represents two points dropped for United, who conceded a late equaliser against Leicester on Saturday.
Jose Mourinho’s side are 12 points behind Premier League leaders Manchester City, who play Newcastle on Wednesday.