diff -u b/core/modules/views/templates/views-view-grid.html.twig b/core/modules/views/templates/views-view-grid.html.twig
--- b/core/modules/views/templates/views-view-grid.html.twig
+++ b/core/modules/views/templates/views-view-grid.html.twig
@@ -9,6 +9,10 @@
  * - view: The view object.
  * - rows: The rendered view results.
  * - options: The view plugin style options.
+ *   - row_class_default: A flag indicating whether default classes should be
+ *   used on rows.
+ *   - col_class_default: A flag indicating whether default classes should be
+ *   used on columns.
  * - items: A list of grid items. Each item contains a list of rows or columns.
  *   The order in what comes first (row or column) depends on which alignment
  *   type is chosen (horizontal or vertical).
diff -u b/core/modules/views/templates/views-view-table.html.twig b/core/modules/views/templates/views-view-table.html.twig
--- b/core/modules/views/templates/views-view-table.html.twig
+++ b/core/modules/views/templates/views-view-table.html.twig
@@ -11,6 +11,8 @@
  *   - attributes: Remaining HTML attributes for the element.
  *   - content: HTML classes to apply to each header cell, indexed by
  *   the header's key.
+ *   - default_classes: A flag indicating whether default classes should be
+ *   used.
  * - caption_needed: Is the caption tag needed.
  * - caption: The caption for this table.
  * - accessibility_description: Extended description for the table details.
@@ -20,6 +22,8 @@
  *   - columns: Row column items. Columns are keyed by column number.
  *     - attributes: HTML classes to apply to each column.
  *     - content: The column content.
+ *   - default_classes: A flag indicating whether default classes should be
+ *   used.
  * - responsive: A flag indicating whether table is responsive.
  * - sticky: A flag indicating whether table header is sticky.
  *
@@ -60,8 +64,16 @@
   {% if header %}
     <thead>
       <tr>
-        {% for column in header %}
-          <th{{ column.attributes }} scope="col">
+        {% for key, column in header %}
+          {% if column.default_classes %}
+            {%
+              set column_classes = [
+                'views-field',
+                'views-field-' ~ fields[key],
+              ]
+            %}
+          {% endif %}
+          <th{{ column.attributes.addClass(column_classes) }} scope="col">
             {{ column.content }}
           </th>
         {% endfor %}
@@ -71,8 +83,16 @@
   <tbody>
     {% for row in rows %}
       <tr{{ row.attributes }}>
-        {% for column in row.columns %}
-          <td{{ column.attributes }}>
+        {% for key, column in row.columns %}
+          {% if column.default_classes %}
+            {%
+              set column_classes = [
+                'views-field',
+                'views-field-' ~ fields[key],
+              ]
+            %}
+          {% endif %}
+          <td{{ column.attributes.addClass(column_classes) }}>
             {{ column.content }}
           </td>
         {% endfor %}
diff -u b/core/modules/views/templates/views-view-unformatted.html.twig b/core/modules/views/templates/views-view-unformatted.html.twig
--- b/core/modules/views/templates/views-view-unformatted.html.twig
+++ b/core/modules/views/templates/views-view-unformatted.html.twig
@@ -9,6 +9,8 @@
  *   - attributes: The row's HTML attributes.
  *   - content: The row's content.
  * - view: The view object.
+ * - default_row_class: A flag indicating whether default classes should be
+ *   used on rows.
  *
  * @see template_preprocess_views_view_unformatted()
  *
diff -u b/core/modules/views/templates/views-view.html.twig b/core/modules/views/templates/views-view.html.twig
--- b/core/modules/views/templates/views-view.html.twig
+++ b/core/modules/views/templates/views-view.html.twig
@@ -4,14 +4,7 @@
  * Default theme implementation for main view template.
  *
  * Available variables:
- * - attributes: Remaining HTML attributes for the element including:
- *   - class: HTML classes that can be used to style contextually
- *     through CSS, including:
- *     - view
- *     - view-[css_name]
- *     - view-id-[view_name]
- *     - view-display-id-[display_name]
- *     - view-dom-id-[dom_id]
+ * - attributes: Remaining HTML attributes for the element.
  * - css_name: A css-safe version of the view name.
  * - css_class: The user-specified classes names, if any.
  * - header: The optional header.
@@ -31,6 +24,8 @@
  *   view content.
  * - attachment_after: An optional attachment view to be displayed after the
  *   view content.
+ * - dom_id: Unique id for every view being printed to give unique class for
+ *   Javascript.
  *
  * @see template_preprocess_views_view()
  *
diff -u b/core/modules/views/views.theme.inc b/core/modules/views/views.theme.inc
--- b/core/modules/views/views.theme.inc
+++ b/core/modules/views/views.theme.inc
@@ -472,12 +472,9 @@
         $variables['header'][$field]['content'] = \Drupal::l($label, new Url('<current>', [], $link_options));
       }
 
+      $variables['header'][$field]['default_classes'] = $fields[$field]->options['element_default_classes'];
       // Set up the header label class.
       $variables['header'][$field]['attributes'] = array();
-      if ($fields[$field]->options['element_default_classes']) {
-        $variables['header'][$field]['attributes']['class'][] = 'views-field';
-        $variables['header'][$field]['attributes']['class'][] = 'views-field-' . $variables['fields'][$field];
-      }
       $class = $fields[$field]->elementLabelClasses(0);
       if ($class) {
         $variables['header'][$field]['attributes']['class'][] = $class;
@@ -525,12 +522,9 @@
       // Reference to the column in the loop to make the code easier to read.
       $column_reference =& $variables['rows'][$num]['columns'][$column];
 
+      $column_reference['default_classes'] = $fields[$field]->options['element_default_classes'];
       // Add field classes.
       $column_reference['attributes'] = array();
-      if ($fields[$field]->options['element_default_classes']) {
-        $column_reference['attributes']['class'][] = 'views-field';
-        $column_reference['attributes']['class'][] = 'views-field-' . $variables['fields'][$field];
-      }
 
       if ($classes = $fields[$field]->elementClasses($num)) {
         $column_reference['attributes']['class'][] = $classes;