Windows.Web.Http.HttpClientでBasic認証に失敗したときにダイアログが出てきて面食らったので。
var client = new HttpClient();
var req = new HttpRequestMessage(HttpMethod.Post, new Uri("https://hoge.hoge/hoge"));
req.Headers.Authorization = new HttpCredentialsHeaderValue("Basic", CredentialString);
var responese = await client.SendRequestAsync(req);
HttpBaseProtocolFilterクラスのAllowUIプロパティをfalseにして、HttpClientのコンストラクタに渡せばOK。
var filter = new HttpBaseProtocolFilter();
filter.AllowUI = false;
var client = new HttpClient(filter);