Michu's well-placed 58th-minute header - his eighth goal of the season - from Pablo Hernandez's cross set the ball rolling, and they secured the points with three minutes remaining when keeper Tim Krul could only parry substitute Danny Graham's shot and Jonathan de Guzman rifled the rebound home from a tight angle.
Laudrup was understandably delighted by his team's performance, which saw them leapfrog their hosts into 10th place.
"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 after a home loss to West Ham a week ago, 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, and that's very difficult to do as an away team against a team like Newcastle's."