diff -u b/core/modules/comment/comment.module b/core/modules/comment/comment.module
--- b/core/modules/comment/comment.module
+++ b/core/modules/comment/comment.module
@@ -734,7 +734,7 @@
   else {
     $uri = $comment->urlInfo();
     $attributes = $uri->getOption('attributes') ?: array();
-    $attributes += array('rel' => 'bookmark');
+    $attributes += array('class' => array('permalink'), 'rel' => 'bookmark');
     $uri->setOption('attributes', $attributes);
     $variables['title'] = \Drupal::l($comment->getSubject(), $uri);
 
diff -u b/core/modules/comment/templates/comment.html.twig b/core/modules/comment/templates/comment.html.twig
--- b/core/modules/comment/templates/comment.html.twig
+++ b/core/modules/comment/templates/comment.html.twig
@@ -68,7 +68,6 @@
   set classes = [
     'comment',
     status != 'published' ? status,
-    status != 'preview' ? 'permalink',
     not author_id ? 'by-anonymous',
     author_id and author_id == commented_entity.getOwnerId() ? 'by-' ~ commented_entity.getEntityTypeId() ~ '-author',
     'clearfix',
diff -u b/core/themes/bartik/templates/comment.html.twig b/core/themes/bartik/templates/comment.html.twig
--- b/core/themes/bartik/templates/comment.html.twig
+++ b/core/themes/bartik/templates/comment.html.twig
@@ -66,7 +66,6 @@
   set classes = [
     'comment',
     status != 'published' ? status,
-    status != 'preview' ? 'permalink',
     not author_id ? 'by-anonymous',
     author_id and author_id == commented_entity.getOwnerId() ? 'by-' ~ commented_entity.getEntityTypeId() ~ '-author',
     'clearfix',