I would use Nginx as a reverse proxy. There's some information on how to do that Here. Depending on the details of what you're trying to do, you might have a different configuration.
In addition to the tutorial above, here is some more information about Nginx and reverse proxies:
Reverse Proxy Module for Nginx
Reverse Proxy Wikipedia article
The way I would do it for your setup would be to make nginx the default httpd, by having it listen on port 80, then switch your Apache virtual configuration to 8080. Then just follow the links I've provided for a very vanilla style setup. Basically, you'll configure the new URL to forward to your other server in Nginx, then have all other URLs go to 8080, where it will hit your current Apache stack. If you were so inclined, you could move your Apache virtual servers down into the Nginx configs, but its not really necessary. Nginx reverse proxy on top of Apache is a fairly common configuration.