diff --git a/django/contrib/staticfiles/management/commands/collectstatic.py b/django/contrib/staticfiles/management/commands/collectstatic.py
index 2155e37ea6..7004ff0454 100644
--- a/django/contrib/staticfiles/management/commands/collectstatic.py
+++ b/django/contrib/staticfiles/management/commands/collectstatic.py
@@ -107,7 +107,7 @@ class Command(NoArgsCommand):
                     prefixed_path = os.path.join(storage.prefix, path)
                 else:
                     prefixed_path = path
-                found_files[prefixed_path] = storage.open(path)
+                found_files[prefixed_path] = (storage, path)
                 handler(path, prefixed_path, storage)
 
         # Here we check if the storage backend has a post_process
diff --git a/django/contrib/staticfiles/storage.py b/django/contrib/staticfiles/storage.py
index b0f28d4063..0293363fc4 100644
--- a/django/contrib/staticfiles/storage.py
+++ b/django/contrib/staticfiles/storage.py
@@ -198,7 +198,8 @@ class CachedFilesMixin(object):
 
             # use the original, local file, not the copied-but-unprocessed
             # file, which might be somewhere far away, like S3
-            with paths[name] as original_file:
+            storage, path = paths[name]
+            with storage.open(path) as original_file:
 
                 # generate the hash with the original content, even for
                 # adjustable files.
diff --git a/docs/ref/contrib/staticfiles.txt b/docs/ref/contrib/staticfiles.txt
index ce93149cd3..368154cabf 100644
--- a/docs/ref/contrib/staticfiles.txt
+++ b/docs/ref/contrib/staticfiles.txt
@@ -281,8 +281,8 @@ StaticFilesStorage
     .. versionadded:: 1.4
 
     This method is called by the :djadmin:`collectstatic` management command
-    after each run and gets passed the paths of found files, as well as the
-    command line options.
+    after each run and gets passed the local storages and paths of found
+    files as a dictionary, as well as the command line options.
 
     The :class:`~django.contrib.staticfiles.storage.CachedStaticFilesStorage`
     uses this behind the scenes to replace the paths with their hashed