Tabbing through the controls like mad, which people keep suggesting, is of course super-tiring and requires keeping track of the subtle focus indicator—and is not seriously a way to use the keyboard. Instead, there's an app called Shortcat that can activate those controls, with you typing the control's text or a part of it. Like a combination of Vimium and Spotlight. Alas, the app is not free.

Also, personally instead of Spotlight I prefer Alfred, which can replace many shortcuts with commands, which are way more ‘mnemonic’. E.g. locking the screen is ‘scr’ in Alfred for me, which pops up ‘Screen saver’ as the suggestion.