There are multiple options to 'daemonise' a Node.js server, you could use screen or tmux to run the shell in the background - tmux being the my recommended choice in that situation.
If you want to stick to a node.js toolset, the lightest weight option would be forever, however if you're looking for a more advanced solution you should check out pm2.
I used to run processes with a tmux session, I then moved to forever, but found it a chore to use in a multi-user environment, I've been using PM2 for some time now with no issues.
If you're on linux this solution from another StackOverflow user may be worth considering - actually it's probably the best solution of all.