diff -u b/core/includes/update.inc b/core/includes/update.inc
--- b/core/includes/update.inc
+++ b/core/includes/update.inc
@@ -586,6 +586,51 @@
     }
   }
 
+  // A function returning all the updates which directly or indirectly have a
+  // specific update as an edge.
+  $get_all_parents = function($update) use ($graph, &$get_all_parents) {
+    $parents = [];
+    foreach ($graph as $func => $data) {
+      if (isset($data['edges'][$update])) {
+        $parents[] = $func;
+        $parents = array_merge($parents, $get_all_parents($func));
+      }
+    }
+    return $parents;
+  };
+  // If an update U2 has an edge to a system update S then add S as an edge to
+  // all updates having U2 as an edge. This ensures that the chain U1->U2->S
+  // will be executed in that particular order.
+  foreach ($graph as $non_system_func => $data) {
+    if ($data['module'] !== 'system') {
+      if (!empty($data['edges'])) {
+        $sys_updates = [];
+        foreach (array_keys($data['edges']) as $edge) {
+          if ($graph[$edge]['module'] === 'system') {
+            $sys_updates[$edge] = TRUE;
+          }
+        }
+        if ($sys_updates) {
+          foreach ($get_all_parents($non_system_func) as $parent_edge) {
+            $graph[$parent_edge]['edges'] = empty($graph[$parent_edge]['edges']) ? $sys_updates : array_merge($graph[$parent_edge]['edges'], $sys_updates);
+          }
+        }
+      }
+    }
+  }
+  // Find update functions without edges to the system update and add such
+  // updates as edges to the system update as they have to be executed after the
+  // system update.
+  foreach ($graph as $system_function => &$system_data) {
+    if ($system_data['module'] === 'system') {
+      foreach ($graph as $non_system_function => $non_system_data) {
+        if (($non_system_data['module'] !== 'system') && !isset($non_system_data['edges'][$system_function])) {
+          $system_data['edges'][$non_system_function] = TRUE;
+        }
+      }
+    }
+  }
+
   return $graph;
 }