I found the docs for “Dockerizing a Node.js web app” to be helpful, with a small flaw.
The last few lines on that page read:
If you use Docker Machine on OS X, the port is actually mapped to the Docker host VM, and you should use the following command:
$ curl $(docker-machine ip VM_NAME):49160
It took me some digging to understand that VM_NAME could be found via the docker-machine ls command, and (for the beginner) would almost always be default.