Can I log in to Google from node.js using username/password?

I have a Google account just for my application that can send email on behalf of my application. We'll call it myservice@gmail.com. It works like this:

1. User logs in with their own Google account
2. User performs an action which requires notification
3. Nodejs sends an email as myservice@gmail.com. It is important to note that nodemailer does this with myservice@gmail.com's username and password.

I want to do something similar with Calendar. I want nodejs to create/delete/share calendars and events on myservice@gmail.com's Calendar.

I've tried this using a service account from the Google Developer Console, but can't seem to get the authentication to work, and don't know how to give the service account access to myservice.gmail.com's calendar.

As a different approach, can I do something similar to Nodemailer? Can I access the account directly from nodejs with a username and password and use the googleapis this way?