Is there a way to enable Performance Counters to monitor Node.js application performance in Windows Azure?
I haven't experimented with it myself yet, but there is node-perfmon which is a wrapper around typeperf. That says it allows you to write performance counters, as well as simple memory / cpu monitoring. Is this the sort of monitoring you were looking for?
Just adding more to above answers..
For application stats monitoring on Node.js you can use Hummingbird. It supports status over http so you can integrate the code in your node.js app add one port to get the monitoring data over HTTP. No need to use Azure Storage Diagnostics and all info in real time in same machine. It's still in pre-alfa, but is handling with few tasks really well.
http://projects.nuttnet.net/hummingbird/
I know about the node.js "monitor" plugin which is the best for Linux machines for system specific performance and also use HTTP to provide system specific data. I am not sure if that can be ported to Windows Server but if can that is one great choice. Read more about monitor usage here: http://www.sys-con.com/node/2275314
You may want to also look at these, they aren't directly using perfmon, but allow you to monitor the performance of your Node.js server:
http://search.npmjs.org/#/Probes.js
http://search.npmjs.org/#/nodetime
The NPM registry is a great tool for finding Node.js packages.