diff -r 5c76f787e695 Lib/test/test_ordered_dict.py
--- a/Lib/test/test_ordered_dict.py	Mon Jul 25 00:31:54 2016 -0400
+++ b/Lib/test/test_ordered_dict.py	Mon Jul 25 22:10:54 2016 +0800
@@ -97,6 +97,40 @@
         self.assertRaises(TypeError, OrderedDict().update, (), ())
         self.assertRaises(TypeError, OrderedDict.update)
 
+        # Make sure update obeys MutableMapping.update's invoking sequence
+        class X:
+            def __init__(self):
+                self.seq = pairs
+                self.index = 0
+            def __getitem__(self, key):
+                for item in self.seq:
+                    if key == item[0]:
+                        return item[1]
+                raise KeyError
+            def __iter__(self):
+                return self
+            def __next__(self):
+                if self.index == len(self.seq):
+                    raise StopIteration
+                else:
+                    result = self.seq[self.index]
+                    self.index += 1
+                    return result
+            def keys(self):
+                return [item[0] for item in self.seq[:-1]]
+            # should not be invoked, issue #27576
+            def items(self):
+                return self.seq[:1]
+        # invoking .keys() first
+        od = OrderedDict()
+        od.update(X())
+        self.assertEqual(list(od.items()), pairs[:-1])
+        # if no .keys(), treat as pair input
+        od = OrderedDict()
+        del X.keys
+        od.update(X())
+        self.assertEqual(list(od.items()), pairs)
+
     def test_fromkeys(self):
         OrderedDict = self.OrderedDict
         od = OrderedDict.fromkeys('abc')
diff -r 5c76f787e695 Objects/odictobject.c
--- a/Objects/odictobject.c	Mon Jul 25 00:31:54 2016 -0400
+++ b/Objects/odictobject.c	Mon Jul 25 22:10:54 2016 +0800
@@ -2337,7 +2337,6 @@
 {
     int res = 0;
     Py_ssize_t len;
-    _Py_IDENTIFIER(items);
     _Py_IDENTIFIER(keys);
 
     /* first handle args, if any */
@@ -2353,22 +2352,7 @@
         PyObject *other = PyTuple_GET_ITEM(args, 0);  /* borrowed reference */
         assert(other != NULL);
         Py_INCREF(other);
-        if (PyDict_CheckExact(other) ||
-            _PyObject_HasAttrId(other, &PyId_items)) {  /* never fails */
-            PyObject *items;
-            if (PyDict_CheckExact(other))
-                items = PyDict_Items(other);
-            else
-                items = _PyObject_CallMethodId(other, &PyId_items, NULL);
-            Py_DECREF(other);
-            if (items == NULL)
-                return NULL;
-            res = mutablemapping_add_pairs(self, items);
-            Py_DECREF(items);
-            if (res == -1)
-                return NULL;
-        }
-        else if (_PyObject_HasAttrId(other, &PyId_keys)) {  /* never fails */
+        if (_PyObject_HasAttrId(other, &PyId_keys)) {  /* never fails */
             PyObject *keys, *iterator, *key;
             keys = _PyObject_CallMethodIdObjArgs(other, &PyId_keys, NULL);
             if (keys == NULL) {