This is exactly what Screenshot Captor was designed for.
As Tomos says, you just have to go to the options (via tray, quick capture bar, on main options dialog on Interface tab) and tell it to stay minimized after capture.
Then SC will do what it always does, automatically save and name image files.
You can also customize how image files are named if you prefer something other than the default naming scheme of using the current date and time.