I dont have any problems on logging in into my Binance account and 2fa works perfectly.
The 2FA where the problem lies. @OP, I know this is just a small mistake but does your google authenticator has other apps registered? because I have this mistake many times that I've looked wrongly to the code and input it (made me worried) which should be for the other registered app on the authenticator.
This is why its important to rename so that you would able to recognize which one. 
Have you tried to sync the app? If not, you can do that by going to Settings > Time correction for code > Sync now.
This one works and op should try it out.
The 2FA where the problem lies. @OP, I know this is just a small mistake but does your google authenticator has other apps registered? because I have this mistake many times that I've looked wrongly to the code and input it (made me worried) which should be for the other registered app on the authenticator.
Have you tried to sync the app? If not, you can do that by going to Settings > Time correction for code > Sync now.