That style of URL (domain.tld/resource/path) would need to be handled via mod_rewrite (with Apache) or a try_files configuration with Nginx. Which you use depends on which HTTP server you're running, of course. Unless you're explicitly setup Nginx, it's probably Apache.
Assuming Apache (httpd) is being used- The easiest method to manage this is via a .htaccess file in your document root (where your index.php file lives). You'll need to verify mod_rewrite is enabled in your httpd configuration (usually found at /etc/httpd/httpd.conf or broken out further in a subdirectory).
There are a lot of configuration options available to you via mod_rewrite. Here's an example of one that will translate all URLs that do not point to an actual directory or file (thus preserving your ability to serve static content directly from httpd) to index.php:
<IfModule mod_rewrite.c>
RewriteEngine On
RewriteBase /
RewriteRule ^index.php$ - [L]
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule . /index.php [L]
</IfModule>
You would need to parse the URL to determine what to do with it (it will be contained within $_SERVER['REQUEST_URI']. Be sure to reference the mod_rewrite documentation if you need to make changes to this configuration.