There is indeed a command line tool that is exactly built for your use case - have a look at WuInstall (http://www.wuinstall.com) - it is a commercial product intended for companies with 50 machines and more but you can always download a free trial version to test in your environment
You can put wuinstall.exe in a batch script on the same machine or you can call it remotely via psexec
In the simplest case (you will also probably need a few more options for pruction environments) just write your batch script calling
wuInstall /install /reboot_if_needed
and kick it of with a task scheuduler of your choice at the time you want to update.
With the /reboot_if_needed option it is possible to reboot the machine unattended after the update, and the /rebootcylce option even reboots multiple times until all updates are installed.
WuInstall basically puts the whole Windows Update API and its most common use cases in one central command line tool - There are quite a few more options to script and select windows updates, check out the technical documentation under: https://wuinstall.atlassian.net/wiki/display/WD/WuInstall+HowTo