diff --git a/core/modules/contextual/lib/Drupal/contextual/Plugin/views/field/ContextualLinks.php b/core/modules/contextual/lib/Drupal/contextual/Plugin/views/field/ContextualLinks.php
index e6ce0ad..56585a5 100644
--- a/core/modules/contextual/lib/Drupal/contextual/Plugin/views/field/ContextualLinks.php
+++ b/core/modules/contextual/lib/Drupal/contextual/Plugin/views/field/ContextualLinks.php
@@ -71,7 +71,8 @@ function pre_render(&$values) {
   function render($values) {
     $links = array();
     foreach ($this->options['fields'] as $field) {
-      if (empty($this->view->style_plugin->rendered_fields[$this->view->row_index][$field])) {
+      $rendered_field = $this->view->style_plugin->get_field($this->view->row_index, $field);
+      if (empty($rendered_field)) {
         continue;
       }
       $title = $this->view->field[$field]->last_render_text;
diff --git a/core/modules/views/lib/Drupal/views/Plugin/views/style/StylePluginBase.php b/core/modules/views/lib/Drupal/views/Plugin/views/style/StylePluginBase.php
index abed751..274ff1f 100644
--- a/core/modules/views/lib/Drupal/views/Plugin/views/style/StylePluginBase.php
+++ b/core/modules/views/lib/Drupal/views/Plugin/views/style/StylePluginBase.php
@@ -80,6 +80,16 @@
   protected $usesFields = FALSE;
 
   /**
+   * Stores the rendered field values, keyed by the row index and field name.
+   *
+   * @see \Drupal\views\Plugin\views\style\StylePluginBase::render_fields()
+   * @see \Drupal\views\Plugin\views\style\StylePluginBase::get_field()
+   *
+   * @var array|null
+   */
+  protected $rendered_fields;
+
+  /**
    * Initialize a style plugin.
    *
    * @param $view
@@ -593,12 +603,12 @@ function render_grouping($records, $groupings = array(), $group_rendered = NULL)
   }
 
   /**
-   * Render all of the fields for a given style and store them on the object.
+   * Renders all of the fields for a given style and store them on the object.
    *
-   * @param $result
+   * @param array $result
    *   The result array from $view->result
    */
-  function render_fields($result) {
+  protected function render_fields(array $result) {
     if (!$this->usesFields()) {
       return;
     }
@@ -622,19 +632,20 @@ function render_fields($result) {
       }
       unset($this->view->row_index);
     }
-
-    return $this->rendered_fields;
   }
 
   /**
-   * Get a rendered field.
+   * Gets a rendered field.
    *
-   * @param $index
+   * @param int $index
    *   The index count of the row.
-   * @param $field
-   *    The id of the field.
+   * @param string $field
+   *   The ID of the field.
+   *
+   * @return string|null
+   *   The output of the field, or NULL if it was empty.
    */
-  function get_field($index, $field) {
+  public function get_field($index, $field) {
     if (!isset($this->rendered_fields)) {
       $this->render_fields($this->view->result);
     }
diff --git a/core/modules/views/lib/Drupal/views/Tests/Handler/FieldCounterTest.php b/core/modules/views/lib/Drupal/views/Tests/Handler/FieldCounterTest.php
index ce5599a..b9a6cba 100644
--- a/core/modules/views/lib/Drupal/views/Tests/Handler/FieldCounterTest.php
+++ b/core/modules/views/lib/Drupal/views/Tests/Handler/FieldCounterTest.php
@@ -54,11 +54,11 @@ function testSimple() {
     ));
     $view->preview();
 
-    $counter = $view->style_plugin->rendered_fields[0]['counter'];
+    $counter = $view->style_plugin->get_field(0, 'counter');
     $this->assertEqual($counter, 1, format_string('Make sure the expected number (@expected) patches with the rendered number (@counter)', array('@expected' => 1, '@counter' => $counter)));
-    $counter = $view->style_plugin->rendered_fields[1]['counter'];
+    $counter = $view->style_plugin->get_field(1, 'counter');
     $this->assertEqual($counter, 2, format_string('Make sure the expected number (@expected) patches with the rendered number (@counter)', array('@expected' => 2, '@counter' => $counter)));
-    $counter = $view->style_plugin->rendered_fields[2]['counter'];
+    $counter = $view->style_plugin->get_field(2, 'counter');
     $this->assertEqual($counter, 3, format_string('Make sure the expected number (@expected) patches with the rendered number (@counter)', array('@expected' => 3, '@counter' => $counter)));
     $view->destroy();
 
@@ -81,13 +81,13 @@ function testSimple() {
     ));
     $view->preview();
 
-    $counter = $view->style_plugin->rendered_fields[0]['counter'];
+    $counter = $view->style_plugin->get_field(0, 'counter');
     $expected_number = 0 + $rand_start;
     $this->assertEqual($counter, $expected_number, format_string('Make sure the expected number (@expected) patches with the rendered number (@counter)', array('@expected' => $expected_number, '@counter' => $counter)));
-    $counter = $view->style_plugin->rendered_fields[1]['counter'];
+    $counter = $view->style_plugin->get_field(1, 'counter');
     $expected_number = 1 + $rand_start;
     $this->assertEqual($counter, $expected_number, format_string('Make sure the expected number (@expected) patches with the rendered number (@counter)', array('@expected' => $expected_number, '@counter' => $counter)));
-    $counter = $view->style_plugin->rendered_fields[2]['counter'];
+    $counter = $view->style_plugin->get_field(2, 'counter');
     $expected_number = 2 + $rand_start;
     $this->assertEqual($counter, $expected_number, format_string('Make sure the expected number (@expected) patches with the rendered number (@counter)', array('@expected' => $expected_number, '@counter' => $counter)));
   }
diff --git a/core/modules/views/lib/Drupal/views/ViewExecutable.php b/core/modules/views/lib/Drupal/views/ViewExecutable.php
index f2fe9b2..7c8c6c4 100644
--- a/core/modules/views/lib/Drupal/views/ViewExecutable.php
+++ b/core/modules/views/lib/Drupal/views/ViewExecutable.php
@@ -1358,27 +1358,6 @@ public function render($display_id = NULL) {
   }
 
   /**
-   * Render a specific field via the field ID and the row #
-   *
-   * Note: You might want to use views_plugin_style::render_fields as it
-   * caches the output for you.
-   *
-   * @param string $field
-   *   The id of the field to be rendered.
-   *
-   * @param int $row
-   *   The row number in the $view->result which is used for the rendering.
-   *
-   * @return string
-   *   The rendered output of the field.
-   */
-  public function renderField($field, $row) {
-    if (isset($this->field[$field]) && isset($this->result[$row])) {
-      return $this->field[$field]->advanced_render($this->result[$row]);
-    }
-  }
-
-  /**
    * Execute the given display, with the given arguments.
    * To be called externally by whatever mechanism invokes the view,
    * such as a page callback, hook_block, etc.
diff --git a/core/modules/views/theme/theme.inc b/core/modules/views/theme/theme.inc
index 81cd0e6..e5b72a3 100644
--- a/core/modules/views/theme/theme.inc
+++ b/core/modules/views/theme/theme.inc
@@ -478,10 +478,6 @@ function template_preprocess_views_view_table(&$vars) {
     $query += $view->exposed_raw_input;
   }
 
-  // Fields must be rendered in order as of Views 2.3, so we will pre-render
-  // everything.
-  $renders = $handler->render_fields($result);
-
   foreach ($columns as $field => $column) {
     // Create a second variable so we can easily find what fields we have and what the
     // CSS classes should be.
@@ -577,7 +573,7 @@ function template_preprocess_views_view_table(&$vars) {
       $vars['field_attributes'][$field][$num] = array();
 
       if (!empty($fields[$field]) && empty($fields[$field]->options['exclude'])) {
-        $field_output = $renders[$num][$field];
+        $field_output = $handler->get_field($num, $field);
         $element_type = $fields[$field]->element_type(TRUE, TRUE);
         if ($element_type) {
           $field_output = '<' . $element_type . '>' . $field_output . '</' . $element_type . '>';