diff --git a/django/template/base.py b/django/template/base.py
index ed4196012a..382b85aefd 100644
--- a/django/template/base.py
+++ b/django/template/base.py
@@ -6,7 +6,7 @@ from importlib import import_module
 from inspect import getargspec
 
 from django.conf import settings
-from django.template.context import (Context, RequestContext,
+from django.template.context import (BaseContext, Context, RequestContext,
     ContextPopException)
 from django.utils.itercompat import is_iterable
 from django.utils.text import (smart_split, unescape_string_literal,
@@ -765,6 +765,9 @@ class Variable(object):
                     current = current[bit]
                 except (TypeError, AttributeError, KeyError, ValueError):
                     try:  # attribute lookup
+                        # Don't return class attributes if the class is the context:
+                        if isinstance(current, BaseContext) and getattr(type(current), bit):
+                            raise AttributeError
                         current = getattr(current, bit)
                     except (TypeError, AttributeError):
                         try:  # list-index lookup
diff --git a/tests/template_tests/test_context.py b/tests/template_tests/test_context.py
index ca167a73f3..7bcfb7f9f2 100644
--- a/tests/template_tests/test_context.py
+++ b/tests/template_tests/test_context.py
@@ -2,7 +2,7 @@
 
 from unittest import TestCase
 
-from django.template import Context
+from django.template import Context, Variable, VariableDoesNotExist
 
 
 class ContextTests(TestCase):
@@ -25,3 +25,12 @@ class ContextTests(TestCase):
         with c.push(a=3):
             self.assertEqual(c['a'], 3)
         self.assertEqual(c['a'], 1)
+
+    def test_resolve_on_context_method(self):
+        # Regression test for #17778
+        empty_context = Context()
+        self.assertRaises(VariableDoesNotExist,
+                Variable('no_such_variable').resolve, empty_context)
+        self.assertRaises(VariableDoesNotExist,
+                Variable('new').resolve, empty_context)
+        self.assertEqual(Variable('new').resolve(Context({'new': 'foo'})), 'foo')