I didn't feel like redeploying vCenter Server Appliance, so I took a risk and edited the raw linux networking config. Not the approved solution, but it seems to be working fine. If it stops working, then I'm right back where I started (needing to redeploy).
Go to the appliance management page and enable the SSH login and Bash shell:
https://static-ip-address:5480

Then ssh to the appliance. Login as root, and the default password is vmware
. If you set a password for the appliance for the web client, then use that password with the root username.
Connected to service
* List APIs: "help api list"
* List Plugins: "help pi list"
* Enable BASH access: "shell.set --enabled True"
* Launch BASH: "shell"
Command>
Launch the shell by typing the command "shell"
shell
edit the interfaces config in linux
vim /etc/sysconfig/networking/devices/ifcfg-eth0
and you should see something like this
DEVICE=eth0
BOOTPROTO='static'
STARTMODE='auto'
TYPE=Ethernet
USERCONTROL='no'
IPADDR='10.8.3.11'
NETMASK='255.255.255.0'
BROADCAST='10.8.3.255'
Make the changes you want, then restart the networking service.
localhost:~ # service network restart
Shutting down network interfaces:
eth0 device: VMware VMXNET3 Ethernet Controller done
Shutting down service network . . . . . . . . . done
Hint: you may set mandatory devices in /etc/sysconfig/network/config
Setting up network interfaces:
eth0 device: VMware VMXNET3 Ethernet Controller
eth0 IP address: 10.8.3.11/21 done
Setting up service network . . . . . . . . . . done