Please paste a snippet that shows it doesn't work.
Thanks!

The script used for testing is as follows:

<?php
$db=new mysqli("localhost", "root", PASSWORD);
if($db->connect_errno !== 0) {
	exit("Unable to connect to database: ".$db->connect_error);
}
echo "Connected";
$db->close();
?>

Result:

Warning: mysqli::mysqli(): (HY000/2002): No connection could be made because the target machine actively refused it.
Unable to connect to database: No connection could be made because the target machine actively refused it.

Remarks:

The database has enable-named-pipe and skip-networking in effect.

I don't want to be rude. Please read, the MySQL documentation. When you want to use named pipes your host should not be "localhost". "localhost" has a special meaning only on Unix(-like) systems, where it means "use unix socket file", while on windows it will be resolved as 127.0.0.1 and TCP connection will be tried to be established.

On Windows, to use named pipes, you should use "." (dot) as host, which will in turn use the default named pipe name \\.\pipe\MySQL (if you use the name in your code you should escape the slashes, if you use double quotes "\\\\.\\pipe\\MySQL".
Please try this and report your success or failure.

When using "." as the hostname, the following warning is returned:

Warning: mysqli::mysqli(): (HY000/2002): Unknown errror while connecting

When using "\\\\.\\pipe\\MySQL". as the hostname, the following error is returned:

php_network_getaddresses: getaddrinfo failed: No such host is known.

Regarding documentation, if "." is required for named pipe connection, the PHP documentation, not the MySQL documentation, should explicitly state so. Currently, it only states "Can be either a host name or an IP address. Passing the NULL value or the string "localhost" to this parameter, the local host is assumed. When possible, pipes will be used instead of the TCP/IP protocol.", I expected that passing "localhost" will cause pipes to be used when possible, and did not expect "." is supported as it is not a valid hostname or IP address.

Changed affected PHP version to 5.4.1.

Can you connect to MySQL using named pipe and the mysql prompt (http://dev.mysql.com/doc/refman/5.5/en/connecting.html)?

Yes, I am able to connect using the following command:

mysql -W -u root -p

Finally, I found that the connection problem is caused by the use of open_basedir. It appears that named pipe cannot be used with open_basedir.

I have changed the type of this report to be documentation problem. I think the documentation should mention that:

- "." should be used instead of "localhost" for named pipe connection
- Named pipe will fail when open_basedir is in effect

Thanks for following up and changing to doc problem. Great hint on open basedir... mysqlnd is using PHP Streams and PHP Stream will follow PHP rules.

I have this problev when <mysqli.default_socket="mysql"> and use msqli.
To solve need cleanup this parameter <mysqli.default_socket=>

sorry, "this problem" :)
change need make in file <php.ini>

====more complete instructions to solve this problem on windows platform====
============================================================================
in file <php.ini>, or another config php files if use, need follower:

mysql.default_socket=
mysqli.default_socket=


in file <my.ini>, or another config mysql files if use, need follower:

socket = mysql
============================================================================
It's all :)