Burnley were on the undeserving end of ruthless finishing, despite an impressive away performance at Old Trafford.
Danny Ings had offered hope of a result after his diving header brought the Clarets back on level terms, after substitute Chris Smalling had given Manchester United an early lead.
However, another header from Smalling in first-half stoppage time and a late penalty courtesy of Robin van Persie sealed the victory for the hosts.
Burnley though could leave Old Trafford with heads held high though, having put United under severe pressure for large parts of the encounter.
Sean Dyche made a change to his starting line-up for the first time in 11 games as Michael Kightly replaced the injured Dean Marney.
Scott Arfield moved across to partner David Jones in the centre of midfield.
Meanwhile, Louis van Gaal kept faith in his diamond formation with Wayne Rooney, Ángel Di María, Radamel Falcao and van Persie all starting for Manchester United.
Burnley were first to create a goalscoring chance after less than three minutes.
On his first return to Old Trafford, Michael Keane got away from Phil Jones, but couldn’t direct his header on target from Kieran Trippier’s in-swinging corner.
In response, Tom Heaton did well to push aside Paddy McNair’s dangerous effort from outside the box.
However, United went in front from the resulting corner.
Van Persie won the first header at the near post and Falcao knocked the ball back across the face of goal before Smalling – who had just replaced the injured Jones – rose highest to head the ball into the far corner of the net with his first touch.
But there could have been little doubt about the strength of the Clarets’ character.
On nine minutes, Ings turned with the ball sharply and released Kightly away down the left wing. The winger tried his luck from a tight angle only for de Gea to produce a good save.
Three minutes later though, Burnley were level.
Trippier did superbly to collect the second ball and drive down the right flank before whipping in a wonderful cross that Ings headed home beautifully on the stretch.
It was the England under-21 international’s ninth goal of the season - and fifth in his last six matches!
Such was the intensity to the Clarets’ performance that they twice went close to turning the score around soon after.
First, Ings saw his side-foot shot blocked following another corner.
And two minutes later, Trippier played Ings through into the channel with an inch-perfect long pass, before the latter pulled the ball back to Barnes, whose first-time effort flew just wide of the post.
Burnley kept causing United problems throughout the first half with their energy and high pressing as well as Trippier’s consistently outstanding deliveries.
And on 37 minutes, Ings and Trippier combined again, with Barnes heading the resulting ball into the box over the crossbar at the near post.
It was United who came off the pitch for the break ahead against the run of play, though.
Rooney and Di María played a clever, short corner and Smalling jumped up highest once more to head the ball home and restore the hosts’ lead three minutes into the first-half stoppage time.
Straight after the restart, the Clarets looked to continue their very good showing.
Two minutes into the half, Trippier and Ings linked up with George Boyd this time with de Gea then making himself big to deny Ings at point-blank range.
It was to prove a pivotal moment as United then began to work their way into the game.
At the other end, Adnan Januzaj forced a comfortable save from Heaton after driving at the Burnley defence on 56 minutes.
And although the Clarets kept asking questions of the opposition backline, United finally recorded a prolonged spell of possession after van Gaal moved Januzaj and Di María to the wings to provide more width.
The hosts also defended deeper and controlled space better as the match wore on, restricting Burnley’s opportunities.
The Clarets never stopped going and when Kightly saw his powerful strike deflected behind for a corner, the vocal travelling support could sense an equaliser coming.
It wasn’t the night, though and with eight minutes left on the clock, Di María sprinted into the box on the counter-attack before the referee adjudged he was brought down by Arfield.
Van Persie calmly dispatched the resulting spot-kick.
Jason Shackell then cleared the ball of the goal-line late on to deny Januzaj and United their fourth.
Burnley: Heaton; Trippier, Keane, Shackell, Mee; Boyd, Arfield, Jones, Kightly (Vokes 86); Ings, Barnes (Jutkiewicz 90+2).
Subs not used: Gilks, Duff, Lafferty, Reid, Wallace.
Man United: de Gea; McNair, Jones (Smalling 5), Evans, Rojo; Blind (Herrera 39); Rooney, Di María; Januzaj; Falcao (Wilson 73), van Persie.
Subs not used: Valdés, Valencia, Mata, Fellaini.
Goals: Smalling 6, 45+3, van Persie 82-pen – Ings 12
Bookings: Rooney, Falcao, Wilson, Di María – Kightly, Mee, Arfield
Referee: Kevin Friend