How to save media-form on custom tab

Just figured out this one– in the function that load the iframe, add this:

if ( !empty($_POST) ) {
    $return = media_upload_form_handler();

    if ( is_string($return) )
        return $return;
    if ( is_array($return) )
        $errors = $return;
}

Then, all the form data get saved as normal.