Hi!
I’m glad you like DigitalOcean. :)

Yes this is possible. Usual set up is to run Node app on non 80 ports (for example 8080, 3000, you can use any greeter than 1024) and make reverse proxy with Nginx or Apache to port 80.
This is done because to run something on port less than 1024 you need to run it with with root privileges. That’s why you usually want to run it on any port greeter than 1024 then use reverse proxy to make it work on 80.

DigitalOcean covered you for Node.js + Nginx in How To Set Up a Node.js Application for Production on Ubuntu 16.04.
About Apache, I think there is no direct tutorial for Node.js but How to Set Up Apache Traffic Server as a Reverse-Proxy on Ubuntu 14.04. It is for Ubuntu 14.04 but is also relevant for 16.04.
I really recommend to read Nginx one also, it’s great one. Pay attention to pm2 part, it’s Nodejs service management plug in that will help a lot.

If you got any question, feel free to ask, I’ll or somebody other will try to give you answer. :)