Install an external plugin within the current plugin

I'm trying to install an additional plugin, and all I have is the slug name of the plugin under api.wordpress.org. I've figured out that one could get the zip file's path (download_link) when going to http://ift.tt/1BzobcD

What would be the rest? I wouldn't want to do the entire unzipping if there's a built-in function in WP that does that...?