I did some testing, and found that a memory dump of Chrome doesn't hold the password of gmail.com/Google after logging in to that site (the login happens on accounts.google.com).
(My System is Windows 10 64bit Professional, Chrome 60).
I can find the passwords of all other sites I've tested. Also when I do the same in Firefox, the gmail.com password will be stored in the memory dump. This is a Chrome-specific behaviour.
I've tried a lot of things to prevent the password from being stored in a memory-dump. Even when I hash the password in the password-field before submitting the form, the original (un-hashed) password will be contained in the memory dump. I tried with autocomplete="off", I tried sending the password through a 'hidden' field, and an invisible text field. (So that the browser won't attempt to store the password in the built-in password-manager).
I've also - of course - tried with deactivated password-storage, cleared the cache, experimented with Cache-Control/Pragma/Expires -headers, and what not. And I know that the Gmail-website does indeed send the unhashed/original password in the request to the server. So there is no client-side method involved to encrypt/hash/obfuscate the password.
So my question is: whatever gmail.com (accounts.google.com) uses so that the password is not contained in a memory dump, would it be possible to do the same for my own website? Or is that possibly a hardcoded, gmail.com-specific feature of the Chrome-browser?
Could it be coincidence, because that site causes a lot of read-/write-activity on the memory, so that the Garbage Collector cleans up faster, or something like that?