Go directly to Source
Problem:

Recently, while configuring VSTF Version Control Parameters with Dynamics AX 2009, it throwed this error: “The request failed with HTTP Status 405: Method not allowed.”
I was able to browse VSTF folder through IE.

Solution:
This was happening because In version control parameters in AX, I was using port 8090 (Becoz the same port we use when we navigate VSTF Server through IE), When I changed this port to 8080, it started working successfully. This is the port which is used by Team Explorer too.

Make sure to visit the author of this post!