let's assume that package.json looks like this
{
"name": "booyaalolwut",
"version": "6.6.6",
"description": "witty description here",
"scripts": {
"start": "node express/index.js"
},your existing app starts in express/index.js
<?xml version="1.0" encoding="utf-8"?>
<configuration>
<system.webServer>
<handlers>
<add name="iisnode" path="express/index.js" verb="*" modules="iisnode"/> <!-- change path here-->
</handlers>
<rewrite>
<rules>
<rule name="StaticContent">
<action type="Rewrite" url="public{REQUEST_URI}"/>
</rule>
<rule name="DynamicContent">
<conditions>
<add input="{REQUEST_FILENAME}" matchType="IsFile" negate="True"/>
</conditions>
<match url="/*" /> <!-- not sure why this is missing from stock web.config on azure -->
<action type="Rewrite" url="express/index.js" /> <!-- change path to script -->
</rule>
</rules>
</rewrite>
</system.webServer>
</configuration>