Swansea inflicted Man United's first defeat of the season to move up to fourth in the table thanks to goals from in-from forwards Andre Ayew and Bafetimbi Gomis.
Juan Mata scored the opening goal of the game for the away side at the Liberty Stadium but United never truly convinced and allowed the Swans a way back into the game.
The defeat for the Red Devils means four out of last season's top six failed to win this weekend as Chelsea, Liverpool and now United lost, while Tottenham drew.
Mata's goal in the 48th-minute kicked off Louis van Gaal's 50th game in charge of United with a bang. It was a poacher's effort at the back post after he escaped the attentions of City captain Ashley Williams to slide in Luke Shaw's cross on the left side. Incidentally, the Spaniards goal was his 50th in the Premier League.
However, Swansea soon composed themselves and were level in the 60th-minute thanks to Ayew's downward header. It was orchestrated by Williams who intercepted a pass and ran interrupted for 30-yards before finding Gylfi Sigurdsson who crossed from the right to find Ayew who scored his third Premier League goal.
That goal was Gomis' fourth of the season; ninth in the last ten Premier League games and enabled him to become the first Swansea player since Harry Deacon in 1923 to score in the opening four games of the season.