I know it's a 3 year old thread, but maybe somebody (like me) will find this useful.
Make a small folder such as "___Stage" somewhere simple, perhaps at the root of your photo or music storage.
Open that folder in a separate small instance of [windows] explorer on the desktop somewhere. Make it just large enough in visual size to hold a single file in view -- I set about 2 inches square, and set the view mode to large icon to make it big enough to grab without being too accurate.
Drag and drop your internet/firefox/chrome/etc. file to the view pane of that folder.
Drag and drop AGAIN from this folder to your intended destination folder. This will be considered a directory to directory MOVE, which will unlock that magic option #3 "Move new file with (x) appended to rename and keep both files"
Viola.
I tried above just dragging to desktop, but this leaves the file still on the desktop unless you kill the "+" by holding the shift key (or shift mouse button if you have a multibutton mouse set up that way) For some reason win7 considers the desktop different than a directory.
I know this is cludgy, but you never have to take your hand off the mouse, or hunt down the naming conflict and rename it properly.
If you can't stand 01.jpg, 01(1).jpg, 01(2).jpg you'll have to rename them individually. I cannot fathom why win7 removed the #3 option functionality from the COPY option yet includes it in the MOVE option.