The relay alone may work, but I had to solve this same problem more than once, and relays alone would usually "chatter" as the power supply discharged. I built a few small circuits out of a capacitor and two diodes that would shut the relay off immediately. Right now I can't find my schematic drawing. But it's pretty simple, very cheap, and reliable.
I'll find it, and post it.

Of course, if the AC power supply suggested above works, that's probably even simpler.