Open CMD as admin with Windows+R shortcut

The easiest and quickest solution that follows your method, is by starting the command prompt as follows:

Press win to open the start menu. Type in cmd to search for Command Prompt.

Press ctrl+shift+enter to launch Command Prompt as administrator.

This works from Windows 7 and up.

win+r does not natively support this though, but an alternative (and less quick) way, is to type in runas /user:Administrator cmd and then type the password for the administrator account.

EDIT: It seems that the latest version of Windows 10 does offer support for ctrl+shift+enter at the Win+R dialog, so you can now use it there too.

Another fast way is to use Windows+X then hit A.

However I marked the other answer as the correct one because the question originally asked for a way to do that through Windows+R

a simple answer:

1. create a shortcut (LNK) to cmd.exe
2. right-click the shortcut > properties > advanced > [v] run as administratir
3. move the shortcut to a directory on the PATH

now: Win+R > admin > simply hit ok or enter.

nice to have

1. UAC auto-click. it's possible, but WAY out of this scope (and a security break), so I'll press manually Alt+y.
2. system-wide keyboard shortcut that links to this shortcut (or alternative command) directly. I'm using Win+Alt+C

alternative (external) commands

elevate.exe cmd
nircmdc.exe elevatecmd
powershell.exe -command "Start-Process cmd -ArgumentList '/c %CD% && %1 %2 %3 %4 %5' -Verb runas"

(Tested on windows 7)