C# HTTPWebRequest issue with JSON and POST

Hi I am using an api called HubSpot to update lead data on the HubSpot portal.
Here is the link to the Contact Update call -
http://developers.hubspot.com/docs/methods/contacts/update_contact
Here is the way you are supposed to POST -
https://api.hubapi.com/contacts/v1/contact/vid/61571/profile?hapikey=demo

and you pass JSON data like this -

{
  "properties": [
    {
      "property": "lifecyclestage",
      "value": "customer"
    }
  ]
}

I know the code works because if the JSON data is correctly formed everything updates fine and there are no errors
If the JSON data is not formed correctly I get an error 400  -
System.Net.WebException: The remote server returned an error: (400) Bad Request.
When this line is hit -
response = (HttpWebResponse)request.GetResponse();
the C# code immediately hits the "catch" block and my response variable is null -

However, if I If I process the same POST (with improperly formed JSON) using POSTMAN (a Google Chrome plugin), I get more information.  
I still get the error 400 Bad Request, but I actually see return JSON which gives more detail about the error.

{
    "status": "error",
    "message": "[{\"property\":\"Lifecyclestage\",\"msg\":\"Property \\\"Lifecyclestage\\\" does not exist\",\"error\":\"PROPERTY_DOESNT_EXIST\"}]",
    "requestId": "330ed575-902b-4d56-a9d9-2a63499cdaa3"
}

My question is how do I get this returned JSON data in my C# code since the response variable never gets set because it errors out.