This post has been updated on 05 March 2017 for SharePoint Framework 1.0 (GA)
In this post, I have documented how to make an HTTP POST request from your SPFx webpart. There are lots of posts out already which show you how to make a GET request so I will not cover that here. It is fairly straightforward once you understand all the moving parts.
Import the necessary modules in your SPFx webpart code:
Now, the code which makes a POST request to create a list:
And my "Developer workbench" list is created:
Hope this helps.