diff --git a/core/modules/search/search.module b/core/modules/search/search.module
index f2719039376..4e62b099663 100644
--- a/core/modules/search/search.module
+++ b/core/modules/search/search.module
@@ -114,7 +114,6 @@ function search_theme() {
 function search_preprocess_block(&$variables) {
   if ($variables['plugin_id'] == 'search_form_block') {
     $variables['attributes']['role'] = 'search';
-    $variables['attributes']['class'][] = 'container-inline';
   }
 }
 
diff --git a/core/themes/bartik/bartik.theme b/core/themes/bartik/bartik.theme
index 3216ab26569..4d6ef3a1b73 100644
--- a/core/themes/bartik/bartik.theme
+++ b/core/themes/bartik/bartik.theme
@@ -112,10 +112,6 @@ function bartik_preprocess_block(&$variables) {
   if ($variables['plugin_id'] == 'system_branding_block') {
     $variables['attributes']['class'][] = 'clearfix';
   }
-  // Add a container-inline class to keep consistent visual styles
-  if ($variables['plugin_id'] == 'search_form_block') {
-    $variables['content_attributes']['class'][] = 'container-inline';
-  }
 }
 
 /**
diff --git a/core/themes/bartik/templates/block--search-form-block.html.twig b/core/themes/bartik/templates/block--search-form-block.html.twig
new file mode 100644
index 00000000000..b196d4346c5
--- /dev/null
+++ b/core/themes/bartik/templates/block--search-form-block.html.twig
@@ -0,0 +1,23 @@
+{% extends "@classy/block--search-form-block.html.twig" %}
+{#
+/**
+ * @file
+ * Bartik's theme implementation for a search form block. Extends Classy's
+ * search form block template.
+ *
+ * Available variables:
+ * - content: The content of this block.
+ * - content_attributes: A list of HTML attributes applied to the main content
+ *   tag that appears in the template.
+ *
+ * @see template_preprocess_block()
+ * @see search_preprocess_block()
+ *
+ * @ingroup themeable
+ */
+#}
+{% block content %}
+  <div{{ content_attributes.addClass('content', 'container-inline') }}>
+    {{ parent() }}
+  </div>
+{% endblock %}
diff --git a/core/themes/classy/templates/block--search-form-block.html.twig b/core/themes/classy/templates/block--search-form-block.html.twig
new file mode 100644
index 00000000000..399ddd7605c
--- /dev/null
+++ b/core/themes/classy/templates/block--search-form-block.html.twig
@@ -0,0 +1,54 @@
+{#
+/**
+ * @file
+ * Default theme override for the search form block.
+ *
+ * Available variables:
+ * - plugin_id: The ID of the block implementation.
+ * - label: The configured label of the block if visible.
+ * - configuration: A list of the block's configuration values, including:
+ *   - label: The configured label for the block.
+ *   - label_display: The display settings for the label.
+ *   - module: The module that provided this block plugin.
+ *   - cache: The cache settings.
+ *   - Block plugin specific settings will also be stored here.
+ * - block - The full block entity, including:
+ *   - label_hidden: The hidden block title value if the block was
+ *     configured to hide the title ('label' is empty in this case).
+ *   - module: The module that generated the block.
+ *   - delta: An ID for the block, unique within each module.
+ *   - region: The block region embedding the current block.
+ * - content: The content of this block.
+ * - attributes: A list HTML attributes populated by modules, intended to
+ *   be added to the main container tag of this template. Includes:
+ *   - id: A valid HTML ID and guaranteed unique.
+ * - title_attributes: Same as attributes, except applied to the main title
+ *   tag that appears in the template.
+ * - title_prefix: Additional output populated by modules, intended to be
+ *   displayed in front of the main title tag that appears in the template.
+ * - title_suffix: Additional output populated by modules, intended to be
+ *   displayed after the main title tag that appears in the template.
+ *
+ * @see template_preprocess_block()
+ * @see search_preprocess_block()
+ *
+ * @ingroup themeable
+ */
+#}
+{%
+  set classes = [
+    'block',
+    'block-search',
+    'container-inline',
+  ]
+%}
+<div{{ attributes.addClass(classes) }}>
+  {{ title_prefix }}
+  {% if label %}
+    <h2{{ title_attributes }}>{{ label }}</h2>
+  {% endif %}
+  {{ title_suffix }}
+  {% block content %}
+    {{ content }}
+  {% endblock %}
+</div>