Bale firstly set up Jan Vertonghen for Spurs' opener with a lovely lofted pass in the seventh minute, before lashing home his 27th goal of the season for club and country on 21 minutes.
Michu pulled one back for Swansea, but Bale's brilliant block on Nathan Dyer in the final minutes ensured their fightback fell short.
Laudrup said: "There are different levels of players, even at this level.
"There are good players, very good players and exceptional players and they are the ones who sometimes out of nothing can make a difference.
"If you see his goal today, or his goal against West Ham, it was not even a chance. He is a player who makes the difference and you are lucky if you have that. Not many teams do.
"If you take Bale out, without him the teams were at the same level."