I have found examples of running a simple Node only application under an Azure App Service. But for ExpressJS the examples I've found have all used an Azure Cloud Service. New to Azure and just trying to figure out what I should be using.
Simple NodeJS to Azure App Service https://azure.microsoft.com/en-us/documentation/articles/web-sites-nodejs-develop-deploy-mac/
Simple ExpressJS to Azure Cloud Service https://azure.microsoft.com/en-us/documentation/articles/cloud-services-nodejs-develop-deploy-express-app/