diff -u b/core/modules/simpletest/lib/Drupal/simpletest/WebTestBase.php b/core/modules/simpletest/lib/Drupal/simpletest/WebTestBase.php
--- b/core/modules/simpletest/lib/Drupal/simpletest/WebTestBase.php
+++ b/core/modules/simpletest/lib/Drupal/simpletest/WebTestBase.php
@@ -177,6 +177,8 @@
 
   /**
    * Cookies to set on the curl request.
+   *
+   * @var array
    */
   protected $curlCookies = array();
 
@@ -976,8 +978,10 @@
     $this->loggedInUser = FALSE;
     $this->additionalCurlOptions = array();
 
-    // Close the CURL handler.
+    // Close the CURL handler and reset the cookies array used for upgrade
+    // testing so test classes containing multiple tests are not polluted.
     $this->curlClose();
+    $this->curlCookies = array();
   }
 
   /**