I have created a node.js application in Visual Studio 2015 using the Azure SDK 2.7 and the Node.js Tools.
I have successfully set up CI with BitBucket in my web app
You can try to create a instance of "Node JS Empty Web App" from the Gallery at the old portal http://manage.windowsazure.com, see below.
Then, doing the set up deployment from source control at the quick glance of the web app dashboard page to deploy your web app.
Now, browse the web app http:// that works fine.