This is in response to: http://ww.wp.xz.cn/support/topic/how-ca-i-get-widget-id?replies=14 which is closed.
$widget_class = explode( $args['widget_id'] );
$widget_id = $widget_class[ count($widget_class) - 1];
$widget_array = get_option('widget_nameofyourwidget');
$widget_array[$widget_id] = $instance;
update_option('widget_nameofyourwidget', $widget_array);
This allows you to update Widget Options for an instance of a Widget, inside the Widget Function in the Widget class.