Correctly configured DNS works on host but not inside container

We are new to docker and have trouble with DNS resolution inside a container.
The /etc/resolve.conf of both, host and container, is identical and correct (contains the nameserver entry of our sole NS).
Host and container run in the same network. Networking in general is working well inside the container. Our clients can access the services running inside of the container. All is good – but not DNS.
Once we remove entries from the container’s /etc/host, those hosts cannot be found anymore by the container.
Strange but true, it works well on the host.
So there is something inside the container that makes DNS fail.
But what? Any ideas?

Is my question too dumb (i. e. it is answered by RTFM) or is it too complex (i. e. Docker cannot do what we need)?