Invalid zip. How can I send a zip file as stream to the client?

Question

My goal is to create a zip file, add a text file to it, save it as stream and send it over to the client where it can download it.

But when I try to download it, I get an invalid zip file but it has at least more and less the correct size. My guess is that I'm doing something completly wrong with the stream on the client-side.

How can I send a zip file as stream to the client?

Controller that sends the zip file :

var zipFile = new ZipFile();
var stream = new MemoryStream();

zipFile.AddFile("path/to/file");
zipFile.Save(stream);
stream.Seek(0, SeekOrigin.Begin);

var httpResponseMessage = new HttpResponseMessage();
httpResponseMessage.Content = new StreamContent(stream);
httpResponseMessage.Content.Headers.Add("zip-filename", "test_originalfile.zip");
httpResponseMessage.Content.Headers.ContentType = new MediaTypeHeaderValue("application/zip");
httpResponseMessage.Content.Headers.ContentDisposition = new ContentDispositionHeaderValue("attachment");
httpResponseMessage.Content.Headers.ContentDisposition.FileName = "test_originalfile.zip";
httpResponseMessage.StatusCode = HttpStatusCode.OK;
return httpResponseMessage;

Controller that receives it:

$http.get(applicationServerUrl + '/api/UploadedFiles/GetZip?uploadedFileId=' + uploadedFileId)
.success(function (data, status, headers) {
    headers = headers();

    var filename = headers['zip-filename'];
    var contentType = headers['content-type'];

    var linkElement = document.createElement('a');
    try {
        var blob = new Blob([data], { type: contentType });
        var url = window.URL.createObjectURL(blob);

        linkElement.setAttribute('href', url);
        linkElement.setAttribute("download", filename);

        var clickEvent = new MouseEvent("click", {
            "view": window,
            "bubbles": true,
            "cancelable": false
        });
        linkElement.dispatchEvent(clickEvent);
    } catch (ex) {
        console.log(ex);
    }
}).error(function (data) {
    console.log(data);
});