Swansea capitalised on Tim Krul’s poor clearance to take the lead in 58th minute, with Michu netting his seventh goal of the season.
Laudrup’s side extended their lead when Jonathan de Guzman finished from close-range before Demba Ba scored a late consolation on the stroke of full-time.
“I thought it was the best away performance of the season, even better than QPR on the opening day and Liverpool in the cup,” said Laudrup.
“To come to a place like Newcastle when they really needed to get a win after losing last weekend and play like that was excellent.
“We knew that Newcastle were going to make things very difficult for us because they are desperate to climb up the table, but I thought we were superb.
“We kept possession well and some of our counter-attacking was fantastic.
“We scored two, but I can say that we created eight or nine great chances to score.
“The only disappointment was that we conceded right at the end and had to suffer until the final seconds, but I can live with that.”
Get 8/1 enhanced odds on Tottenham to win or 11/1 enhanced odds on Liverpool to win at White Hart Lane on Saturday afternoon. Click here to sign up now. T&Cs apply.
MORE: Latest Man Utd news
MORE: Latest Arsenal news
MORE: The latest football news