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
@@ -87,10 +87,12 @@
           {% if column.default_classes %}
             {%
               set column_classes = [
-                'views-field',
-                'views-field-' ~ fields[key],
+                'views-field'
               ]
             %}
+            {% for field in column.fields %}
+              {% set column_classes = column_classes|merge(['views-field-' ~ field]) %}
+            {% endfor %}
           {% endif %}
           <td{{ column.attributes.addClass(column_classes) }}>
             {{ column.content }}
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
@@ -530,6 +530,11 @@
       $column_reference =& $variables['rows'][$num]['columns'][$column];
 
       $column_reference['default_classes'] = $fields[$field]->options['element_default_classes'];
+
+      // Set the field key to the column so it can be used for adding classes
+      // in a template.
+      $column_reference['fields'][] = $variables['fields'][$field];
+
       // Add field classes.
       if (!isset($column_reference['attributes'])) {
         $column_reference['attributes'] = array();