Php can’t connect to mysql with error 13 (but command line can)

Could not connect: Can’t connect to MySQL server on ‘MYSQL.SERVER’ (13)

This problem is encountered on scientific linux machine or any machine where security patches are applied automatically. The selinux is the reason which does not allow such connections.

setsebool -P httpd_can_network_connect=1

will also be a helpful CLI command to many people visiting this question, as to allow mysql_connet() connections from within HTTP (Apache) requests to a remote MySQL database server, ensure to enable Network Connections from httpd in SElinux usually located in /etc/selinux/config (disabled by default to prevent hackers from attacking other machines using your httpd).