Despite plenty of possession for the hosts, it was Swansea who snatched the points with 15 minutes left to play through Gylfi Sigurdsson's strike.
Here, Sports Mole takes a closer look at the action at the Theatre of Dreams.
On target: 5
On target: 4
Was the result fair?
A defeat was probably harsh on United, but that is not to say that they deserved to come away with the three points. Instead, a draw would have been the fairest result on a strange afternoon at Old Trafford.
Man Utd's performance
If Louis van Gaal thought that he had a squad capable of winning the title, then this display will have raised plenty of questions in the Dutchman's mind. Apart from a decent period of possession following their equaliser in the second half, the home side looked laboured and uninspired for large parts of the match. There was not too much to be critical of from a defensive point of view as debutant Tyler Blackett fitted in well alongside Phil Jones and Chris Smalling, but it was in midfield and attack where the Red Devils really let themselves down. A lack of ideas, energy and dynamism all contributed to a poor showing from the former champions on a day which they will be keen to forget.
Garry Monk should take great pride in the way that his players equipped themselves. Swansea were organised, disciplined and committed, making it difficult for their opponents to break them down. Wilfried Bony did an admirable job leading the attack on his own, while Jonjo Shelvey and Wayne Routledge provided plenty of zip in and around the midfield. However, it was at the back where the Swans excelled thanks to a superb display from captain Ashley Williams. The stoic defender was supremely focused throughout, always ordering his teammates around and making sure that United were given as little space as possible. It is hard to tell what kind of a season they will have from just one match, but more of the same and the South Wales club could be a surprise package.
Sports Mole's man of the match
Ashley Williams: The Swansea captain was a mammoth presence at the back, doing everything that was asked of him. He and his teammates were forced to defend for prolonged periods, particularly in the second half, but Williams played a central role in making sure that they came away with the points. The skipper also showed great awareness in terms of his positioning, constantly looking around him and organising his fellow defenders in order to stifle their opponents.
Wayne Rooney was the only United player that really looked like damaging Swansea, but he stopped his own team from scoring deep in added time when he inadvertently blocked a shot from Adnan Januzaj. The young Belgian's effort looked like it was flying into the net, only for Rooney's body to get in the way and deny the hosts a possible share of the spoils.
Mike Dean was firm but fair during a match that featured a few tasty challenges from both sides. He somehow found a mysterious fifth minute of injury time at the end of the game which could have dented Swansea's hopes of a win, but overall the official put in a competent display.
Man Utd: United continue their Premier League campaign next Sunday when they make the trip to Sunderland.
Swansea: The Swans play their first home match of the season next Saturday against Burnley.