The Magpie browser extension for Password Vault can now fill a login or a two-factor code into the page you are on when you choose Fill or press Ctrl+Shift+L (Command+Shift+L on a Mac). It fills only secure pages on the site the login is saved for. It can also add a login for the current site and change a login's password; the previous password is kept in the login's password history.
The extension is in development and is not yet in the Chrome Web Store or Firefox Add-ons.