diff --git a/core/modules/outside_in/js/outside_in.js b/core/modules/outside_in/js/outside_in.js
index c038cd2..61ad096 100644
--- a/core/modules/outside_in/js/outside_in.js
+++ b/core/modules/outside_in/js/outside_in.js
@@ -12,6 +12,7 @@
   var itemsToToggleSelector = '[data-offcanvas-main-canvas], #toolbar-bar, [data-drupal-outsidein="editable"] a, [data-drupal-outsidein="editable"] button';
   var contextualItemsSelector = '[data-contextual-id] a, [data-contextual-id] button';
   var quickEditItemSelector = '[data-quickedit-entity-id]';
+  var excludedLinksSelector = '[data-outside-in-exclude] [data-outside-in-edit]';
 
   /**
    * Reacts to contextual links being added.
@@ -24,6 +25,9 @@
    * @listens event:drupalContextualLinkAdded
    */
   $(document).on('drupalContextualLinkAdded', function (event, data) {
+    // Remove contextual links that should be excluded.
+    // @see outside_in_block_view_alter().
+    $(excludedLinksSelector).remove();
     // Bind Ajax behaviors to all items showing the class.
     // @todo Fix contextual links to work with use-ajax links in
     //    https://www.drupal.org/node/2764931.
diff --git a/core/modules/outside_in/outside_in.module b/core/modules/outside_in/outside_in.module
index a7fab7b..28f9107 100644
--- a/core/modules/outside_in/outside_in.module
+++ b/core/modules/outside_in/outside_in.module
@@ -55,6 +55,14 @@ function outside_in_block_view_alter(array &$build) {
   $build['#contextual_links']['outside_in'] = [
     'route_parameters' => [],
   ];
+  if (!_outside_in_is_block_editable($build['#plugin_id']) && isset($build['#contextual_links']['block'])) {
+    // If this block should not be editable set an attribute which will be used
+    // to remove the link on the client side.
+    // The individual links are not available here to remove.
+    // @see outside_in.js
+    $build['#attributes']['data-outside-in-exclude'] = TRUE;
+  }
+
 }
 
 /**
@@ -93,7 +101,9 @@ function outside_in_entity_type_build(array &$entity_types) {
 function outside_in_preprocess_block(&$variables) {
   // The main system block does not contain the block contextual links.
   $variables['#cache']['contexts'][] = 'outside_in_is_applied';
-  if ($variables['plugin_id'] !== 'system_main_block' && \Drupal::service('outside_in.manager')->isApplicable()) {
+  /** @var \Drupal\outside_in\OutsideInManagerInterface $outside_in_manager */
+  $outside_in_manager = \Drupal::service('outside_in.manager');
+  if (_outside_in_is_block_editable($variables['plugin_id']) && $outside_in_manager->isApplicable()) {
     // Add class and attributes to all blocks to allow Javascript to target.
     $variables['attributes']['class'][] = 'outside-in-editable';
     $variables['attributes']['data-drupal-outsidein'] = 'editable';
@@ -154,3 +164,18 @@ function outside_in_css_alter(&$css, AttachedAssetsInterface $assets) {
     $css[$path]['group'] = 200;
   }
 }
+
+/**
+ * Checks whether a block is editable by this module.
+ *
+ * @param string $plugin_id
+ *   The plugin ID for the block to check.
+ *
+ * @return bool
+ *   TRUE if the block should have the "Quick Edit" link provided by this
+ *   module.
+ */
+function _outside_in_is_block_editable($plugin_id) {
+  $non_editable_blocks = ['page_title_block', 'system_main_block'];
+  return !in_array($plugin_id, $non_editable_blocks, TRUE);
+}
diff --git a/core/modules/outside_in/tests/src/FunctionalJavascript/OutsideInBlockFormTest.php b/core/modules/outside_in/tests/src/FunctionalJavascript/OutsideInBlockFormTest.php
index c62436c..13b97a5 100644
--- a/core/modules/outside_in/tests/src/FunctionalJavascript/OutsideInBlockFormTest.php
+++ b/core/modules/outside_in/tests/src/FunctionalJavascript/OutsideInBlockFormTest.php
@@ -364,4 +364,27 @@ protected function pressToolbarEditButton() {
     $this->assertSession()->assertWaitOnAjaxRequest();
   }
 
+  /**
+   * Tests that title block does not have a outside_in contextual link.
+   */
+  public function testBlockExcluded() {
+    $web_assert = $this->assertSession();
+    $block = $this->placeBlock('page_title_block');
+    $this->drupalGet('user');
+    // Assert that block has been marked as "editable" and contextual that
+    // should exist does.
+    $web_assert->elementExists('css', "#block-powered[data-drupal-outsidein=\"editable\"] [data-outside-in-edit]");
+    // Check each block that should be excluded.
+    // We do not need to place the main content block.
+    // It's ID will just be 'content'.
+    foreach (["block-{$block->id()}", 'content'] as $excluded_block_id) {
+      // Assert block itself exists.
+      $web_assert->elementExists('css', "#$excluded_block_id");
+      // Assert that exclude block has not been marked as "editable".
+      $web_assert->elementNotExists('css', "#{$excluded_block_id}[data-drupal-outsidein=\"editable\"]");
+      // Assert that contextual that not should exist does not.
+      $web_assert->elementNotExists('css', "#$excluded_block_id [data-outside-in-edit]");
+    }
+  }
+
 }