Burnley stunned the Old Trafford crowd by scoring after just two minutes when after a scramble in the box, Ashley Barnes slammed the ball home under David De Gea.
The home side pushed on for an equaliser but they were caught out 10 minutes before halftime with a brilliant free-kick by Steven Defour which flew into the top corner.
United boss Jose Mourinho responded at half-time with a double change for United as Henrikh Mkhitaryan and Jesse Lingard came on for Marcos Rojo and Zlatan Ibrahimovic.
Lingard missed a guilt edged chance to pull a goal back in the 51 minute when he failed to finish from a few yards out.
But he did put the ball in the net two minutes later with a fine flick into the far corner past Nick Pope.
United pushed on for an equaliser but rarely troubled Pope.
However with the game in stoppage time, Lingard hit a half volley into the right corner from 15 yards.
