Ezvzdump (not to be confused with vzdump) is a shell script that also allows you to dump out a running VE container. The key differences are that ezvzdump allows you to utilize past dumps to speed things up, and that a remote host can be specified to allow backups and tar archiving over the network.

The dump files that are created are compatible with those that vzdump creates, so you must still use vzdump --restore to restore them.

The source code can be downloaded here:
Backup a running container over the network with ezvzdump - OpenVZ Wiki

A further analysis of ezvzdump will be available soon at our planet.admon.org.