Network Manager is managing your resolv.conf. This is the default but there are many ways to change it.
Add dns=no to the [main] section of /etc/NetworkManager/NetworkManager.conf`
Use the Gui: See Below
From Debian Wiki: https://wiki.debian.org/NetworkConfiguration#DNS_configuration_for_NetworkManager
DNS configuration for NetworkManager:
NetworkManager will override dhcp settings, overwriting resolv.conf even if you've configured DNS in /etc/dhcp/dhclient.conf, e.g. causing DNS to first search the local domain, which may have to time out before DNS resolution continues causing lengthy DNS resolution times. You can get an idea of what NetworkManager thinks the settings should be by executing nm-tool at the command line.
You may configure these settings using a GUI by launching nm-connection-editor which currently (13.11.23) isn't to be found in System Tools → Administration menu, rather it must be launched by hand from the command line. After launching:
- Choose a connection (from the Wired or Wireless tab) and click Edit.
- Click on the IPv4 Settings tab
- Choose 'Automatic (DHCP) addresses only' instead of just 'Automatic (DHCP)'.
- Enter the DNS servers in the “DNS servers” field, separated by spaces (e.g. 188.8.131.52 for OpenDNS).
- Click “Apply.”