It sounds like this is corrected in later versions of the OpenVZ kernel but Iam not sure, it may also be that a much newer kernel is needed and Centos may not have a recent enough kernel.
*Debain 7.0 however does work fine as a temporary fix or work around.
Debian 8 OpenVZ no IP and networking not working:
lo Link encap:Local Loopback
If you move your hard drive(s) around to other computers/servers, you'll find that your eth0 keeps getting higher, the first time it will become eth1 and then eth2 etc and even higher if your server has dual or quad NICs. The reason is that udevd basically assigns eth0 tot he first NIC it finds and remembers it, if it encounters a NIC with a differentMAC, it assigns it one higher (eg. eth1).
See the example below, I have eth2 now so how doI fix it?........