@MSStateDawg,

I do not really know how this is programmed into the sites, but I will pass the feedback along if this is something that we can influence.

There is a function in Google Chrome to manually add a site's username and password from the settings, this may be necessary for situations such as this, especially when accessing your router via IP address. This is what I have had to do previously with password managers such as Lastpass to get my router password saved. 

If you are using a TP-Link ID to login, I do not think that Google will be able to make the connection between the two as the TP-Link domain would be completely separate from your local network's domain, you would most likely need to add a separate entry for your router login page.