How to apply patches on Pantheon?

Question

This is specifically a question about Pantheon best-practice workflow, which I'm new to.

I run from a Win7 machine and do not have a full dev environment set up locally: it's just too much hassle to get Windows to play usefully and smoothly as a dev space behind my hosted *nix worlds. So, I am in the habit of developing online.

With Pantheon there is no shell access, but there is git and drush.

I don't use git because the workflow there asssumes that I want to move something off of my local repository up to Pantheon (eg, if I have a local working environment I would apply the patch, then push the patched code to my Pantheon dev), but this is not my usecase.

Using drush seems like an option, but I can't figure out how/if applying a patch is supported.

So...

How to patch a contrib module on Pantheon given no local dev environment?