Switch from inline to external source maps. This avoids several problems with inline source maps in VS 2015 (at least as of Update 3).

templates/WebApplicationBasic/webpack.config.dev.js

@@ -2,6 +2,10 @@ var webpack = require('webpack');
 
 module.exports = {
     plugins: [
-        new webpack.SourceMapDevToolPlugin({ moduleFilenameTemplate: '../../[resourcePath]' }) // Compiled output is at './wwwroot/dist/', but sources are relative to './'
+        // Plugins that apply in development builds only
+        new webpack.SourceMapDevToolPlugin({
+            filename: '[name].js.map', // Remove this line if you prefer inline source maps
+            moduleFilenameTemplate: path.relative('./wwwroot/dist', '[resourcePath]') // Point sourcemap entries to the original file locations on disk
+        })
     ]
 };