diff --git a/django/db/models/lookups.py b/django/db/models/lookups.py
index 010d77a76a..d971ea6380 100644
--- a/django/db/models/lookups.py
+++ b/django/db/models/lookups.py
@@ -6,8 +6,9 @@ from django.utils.functional import cached_property
 
 
 class Extract(object):
-    def __init__(self, lhs):
+    def __init__(self, lhs, lookups):
         self.lhs = lhs
+        self.init_lookups = lookups[:]
 
     def get_lookup(self, lookup):
         return self.output_type.get_lookup(lookup)
diff --git a/django/db/models/sql/query.py b/django/db/models/sql/query.py
index 2832a86fd2..ef7df8552b 100644
--- a/django/db/models/sql/query.py
+++ b/django/db/models/sql/query.py
@@ -1082,26 +1082,27 @@ class Query(object):
 
     def build_lookup(self, lookups, lhs, rhs):
         lookups = lookups[:]
-        lookups.reverse()
         while lookups:
-            lookup = lookups.pop()
+            lookup = lookups[0]
             next = lhs.get_lookup(lookup)
             if next:
-                if not lookups:
+                if len(lookups) == 1:
                     # This was the last lookup, so return value lookup.
                     if issubclass(next, Extract):
-                        lhs = next(lhs)
-                        next = lhs.get_lookup('exact')
-                    return next(lhs, rhs)
+                        lookups.append('exact')
+                        lhs = next(lhs, lookups)
+                    else:
+                        return next(lhs, rhs)
                 else:
-                    lhs = next(lhs)
+                    lhs = next(lhs, lookups)
             # A field's get_lookup() can return None to opt for backwards
             # compatibility path.
-            elif len(lookups) > 1:
+            elif len(lookups) > 2:
                 raise FieldError(
                     "Unsupported lookup for field '%s'" % lhs.output_type.name)
             else:
                 return None
+            lookups = lookups[1:]
 
     def build_filter(self, filter_expr, branch_negated=False, current_negated=False,
                      can_reuse=None, connector=AND):