West Brom as their best display since he took charge of the club.
The Swans took the lead through Michu before Wayne Routledge struck twice.
Romelu Lukaku pulled one back in stoppage time at the end of the first-half, but the South Wales club managed to hold on for the three points.
Laudrup was delighted with the football his side played, hailing it as one of the best performances he has seen in quite some time:
“It was the best (performance) I have seen for several seasons. It is not often as a manager you can sit and enjoy your team playing,” he told SkySports.
“As always during a game there are moments when there are things you have to improve, but the first 45 minutes was outstanding, all 11 players played one-two touch football and everything was so good.
“It was one of the few times I can recall sitting there enjoying the game and
“Today also showed everybody what we can do if we are at our best. It was great for me to see the players at their best.
“The things I will take with me from this game will be the great performance.”