Redhat - Networking - dhclient.conf

Change dhclient.conf

Edit /etc/dhcp3/dhclient.conf

NOTE: You may need to modify /etc/dhcp/dhclient.conf instead of /etc/dhcp3/dhclient.conf

Then find the following line

#prepend domain-name-servers 127.0.0.1;

And change it to

prepend domain-name-servers 8.8.8.8;

This will make dhclient (the DHCP client that NetworkManager uses) prepend this to your dns servers, so resolve.conf will end up looking like this

nameserver 8.8.8.8
nameserver 192.168.1.1

This solution will work everywhere and you will always get the DNS that you have chosen as the primary one.