Goals from Michu and Jonathan De Guzman secured a 2-1 success at Newcastle, who were beaten at home for the second time in a week.
Swansea won at Liverpool in the Capital One Cup, but their only previous away victory in the league was a 5-0 thrashing of QPR on the opening day.
Michael Laudrup: "It was the best away performance this season, including QPR and Liverpool.
"To come here and play Newcastle at a moment when we knew Newcastle really needed a win - because they think they belong much higher than they are now - we knew it would be really difficult for us.
"But we put on a great performance.
"We can always discuss what is a big goal chance, but without my Swansea glasses, I think I can say we created at least eight or nine quite big chances.
"That's very difficult to do as an away team against a team like Newcastle's."
Source: Newcastle United Mad