Looks like DNS setting from OpenVPN profiles configured in network manager are broken in Zesty 
I suspect this is due to the adoption of systemd and its systemd-resolver package which controls all DNS settings. My workaround is to set DNS servers for my VPN connection in /etc/systemd/resolved.conf - this is very cumbersome Any one have similar experience or better workarounds?
I wonder if 16.10 is also affected. I believe it also used systemd-resolved. Do any of these bugs match?
I used 16.10 for about 3 months and had no issues with it. Its only after I upgraded to 17.04 that the DNS troubles began. Some of these bugs expose similar problems - all seems to be caused by systemd-resolver
If you wish to create a bug report in terminal:
ubuntu-bug systemd-resolved
That will take you to launchpad with the necessary information…Launchpad account required.
Since this is not mate specific I would also suggest posting the the Ubuntu Developmental Forum.
Thats all I can think of. Good luck
Thanks for the replys and advice!