In 3b it uses a gezeirah shavah in Ezra-Nehemiah to prove a point. I am certain that in an earlier tractate of the Daf Yomi that it was stated that a gezeirah shavah is only legitimate for Humash and can not be used for Nach. If so, why was this not questioned and how can it stand up?
Barry, I don't remember the quote you mention in your question. Is it possible that you are referring to Bava Kama 2b (and elsewhere), where a Gezeirah Shavah explaining a verse is rejected because "Divrei Torah mi'Divrei Kabalah Lo Yalfinan?" If so, that is not applicable here, since we are not explaining a verse in the torah with this Gezeirah Shavah, but rather another verse in the Navi.
From my research it appears that a gezeirah shavah is only valid within a group of books (the 3 groups are Torah, Neviim and Ketuvim), not between 2 groups. An example of a valid connection is between 2 books of Prophets but not between Humash and Prophets.
Is this your understanding?
I am not familiar with such a principle. (The Gemara only says that we do not derive a law about a verse in the Torah from a Gezeirah Shavah with a verse in Nevi'im or Kesuvim.)