Handle file download from ajax post

Don’t give up so quickly, because this can be done (in modern browsers) using parts of the FileAPI:

var xhr = new XMLHttpRequest();
xhr.open('POST', url, true);
xhr.responseType="blob";
xhr.onload = function () {
    if (this.status === 200) {
        var blob = this.response;
        var filename = "";
        var disposition = xhr.getResponseHeader('Content-Disposition');
        if (disposition && disposition.indexOf('attachment') !== -1) {
            var filenameRegex = /filename[^;=\n]*=((['"]).*?\2|[^;\n]*)/;
            var matches = filenameRegex.exec(disposition);
            if (matches != null && matches[1]) filename = matches[1].replace(/['"]/g, '');
        }

        if (typeof window.navigator.msSaveBlob !== 'undefined') {
            // IE workaround for "HTML7007: One or more blob URLs were revoked by closing the blob for which they were created. These URLs will no longer resolve as the data backing the URL has been freed."
            window.navigator.msSaveBlob(blob, filename);
        } else {
            var URL = window.URL || window.webkitURL;
            var downloadUrl = URL.createObjectURL(blob);

            if (filename) {
                // use HTML5 a[download] attribute to specify filename
                var a = document.createElement("a");
                // safari doesn't support this yet
                if (typeof a.download === 'undefined') {
                    window.location.href = downloadUrl;
                } else {
                    a.href = downloadUrl;
                    a.download = filename;
                    document.body.appendChild(a);
                    a.click();
                }
            } else {
                window.location.href = downloadUrl;
            }

            setTimeout(function () { URL.revokeObjectURL(downloadUrl); }, 100); // cleanup
        }
    }
};
xhr.setRequestHeader('Content-type', 'application/x-www-form-urlencoded');
xhr.send($.param(params, true));

Or if using jQuery.ajax:

$.ajax({
    type: "POST",
    url: url,
    data: params,
    xhrFields: {
        responseType: 'blob' // to avoid binary data being mangled on charset conversion
    },
    success: function(blob, status, xhr) {
        // check for a filename
        var filename = "";
        var disposition = xhr.getResponseHeader('Content-Disposition');
        if (disposition && disposition.indexOf('attachment') !== -1) {
            var filenameRegex = /filename[^;=\n]*=((['"]).*?\2|[^;\n]*)/;
            var matches = filenameRegex.exec(disposition);
            if (matches != null && matches[1]) filename = matches[1].replace(/['"]/g, '');
        }

        if (typeof window.navigator.msSaveBlob !== 'undefined') {
            // IE workaround for "HTML7007: One or more blob URLs were revoked by closing the blob for which they were created. These URLs will no longer resolve as the data backing the URL has been freed."
            window.navigator.msSaveBlob(blob, filename);
        } else {
            var URL = window.URL || window.webkitURL;
            var downloadUrl = URL.createObjectURL(blob);

            if (filename) {
                // use HTML5 a[download] attribute to specify filename
                var a = document.createElement("a");
                // safari doesn't support this yet
                if (typeof a.download === 'undefined') {
                    window.location.href = downloadUrl;
                } else {
                    a.href = downloadUrl;
                    a.download = filename;
                    document.body.appendChild(a);
                    a.click();
                }
            } else {
                window.location.href = downloadUrl;
            }

            setTimeout(function () { URL.revokeObjectURL(downloadUrl); }, 100); // cleanup
        }
    }
});