The Swans' display during the opening 45 minutes was out of the top drawer as a brace of goals from Wayne Routledge and another from Michu set them on their way before Romelu Lukaku pulled one back.
Laudrup said: "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 added: "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 in the first half and the win which means we have 20 points after 14 games and that is really good.
"I will not sit here and say this is the best I have seen in my time but as a manager it is a pleasure to see a team play like that. I have not had that many times, maybe once or twice."
Having watched his side come up well short in their bid to secure a fifth-straight top-flight win for the first time in 34 years, West Brom boss Steve Clarke had no complaints.
He said: "That was very unexpected. We started so slowly it was incredible, you wouldn't believe it.
"We know Swansea are a fantastic team and they play good football and we knew they would cause us problems, but I did not expect so many problems so early and when you are chasing the game it is going to be difficult."
Source: PA