Substitute Luke Moore grabbed his first league goal of the season five minutes from time to give the Swans the three points.
The striker prodded home from close range after Davide Santon's bungled clearance fell into his path, with a deflection off Yohan Cabaye sending the ball beyond Rob Elliot in the Newcastle goal.
The win caps a memorable week for Swansea as they reached the 40-point mark just six days after securing their first major piece of silverware with Capital One Cup success over Bradford at Wembley.
Laudrup was delighted to see his side retain their focus after a week of celebrations, which included Tuesday's victory parade through the streets of the city.
He said: "There was a lot to be pleased about today. Firstly the win and secondly our attitude.
"I spoke in the week about the fact you sometimes see a negative reaction after a big win, but our reaction was an excellent first half where we showed lots of good touches, movement off the ball, and we created chances.
"We went in at 0-0 but we deserved so much more. After that, Newcastle came into the game and had some very good chances but, like us, they did not score when they were at their best and so that late goal decided the game.
"It shows our maturity, sometimes with smaller teams when they do well and get recognition from the media you see a reaction in the game after. You can forget every game starts 0-0.
"I expected what I saw today, but I still had to say it as when you win a cup a negative reaction is normal."
Laudrup was also pleased for Moore, who has found first-team opportunities hard to come by thanks to the sensational performances of Michu.
Moore's previous Premier League goal came almost a year ago against Manchester City and Laudrup said: "It is good for Luke to come in and score in a very important game.
"He has helped us to reach 40 points a week after the cup win and it has made this a really great week.
"He has been out of the side for several weeks but when we have rotated the squad we have tended to do well."