My .NET application hosted on IIS stop working after deploying NODE

It is indeed always a complex task!! You can brief a little more on what is your purpose of the Node deployment here..

Two things, either you can set the URL re-write to point to the config file of the app

or 

Create a site in the IIS, then "npm run build" in the server to create a build folder and point the site's physical location to that build folder.