Javier Hernandez scored the only goal in the 11th minute in South Wales from a cross by Welshman Ryan Giggs to inflict a first home defeat on the Premier League newcomers.
United were never at their best against a Swansea side whose passing game impressed United manager Alex Ferguson but rarely looked troubled at the back apart from one let-off in the first half when Scott Sinclair mis-kicked in front of goal.
Unbeaten record
Huddersfield Town are closing in on Arsenal's English record unbeaten league run after moving up to second on the list with a 2-1 victory over Notts County on Saturday -- their 43rd match without defeat.
The League One (third division) club, a dominant force in the 1920s when they collected three top-flight titles, have won 25 games and drawn 18 since Dec 28.
Arsenal's 'Invincibles' hold the record after going 49 matches without losing. They went through the whole of the 2003-04 Premier League season undefeated. Huddersfield have now moved ahead of Nottingham Forest who went 42 games unbeaten under Brian Clough during the 1977-78 and 78-79 seasons.
That still stood as the English Football League record because Forest's dominance came before the Premier League was launched.
"This run will go down in history," Huddersfield chairman Dean Hoyle told the club's website on Saturday. "It will take some time to be broken once again."
Golden Goetze
Borussia Dortmund opened up the Bundesliga title race on Saturday by snatching a 1-0 victory at leaders Bayern Munich with a goal from 19-year-old Mario Goetze.
The day's events were overshadowed though by the suicide attempt from referee Babak Rafati that forced the postponement of the Cologne vs Mainz match.
The 41-year-old failed to show up for the fixture and Cologne police said he was found by his assistants in his hotel room bath with his wrists slit.
"Rafati is out of danger," German FA president Theo Zwanziger told reporters. "He is in a stable condition."
