When this troper saw the movie, he really wondered: How could any man, horny or not, fall for such a stupid act? One should think that a little child would be able to look through her charade.
Perhaps the tagline of another Michael Douglas movie, Disclosure, says it all; Sex is power. Douglas' detective is so enamoured with this woman, so enticed by her, that he basically can't see the forest for the trees, despite being a detective. Tramell's meant to be the perfect femme fatale, and that's how the trope works - older movies are full of men confounded by attractive, dangerous women.
Also, Nick's history suggests he likes to live life on the edge and engage in reckless behavior. He may not care that Catherine is perfectly positioned to kill him. The thrill of courting death could be a powerful rush for him. As she herself puts it, "Nicky got too close to the fire. Nicky liked it."
Plus which, he believes that playing Catherine's game will help him nail the killer.