diff --git a/runtime/autoload/python3complete.vim b/runtime/autoload/python3complete.vim
index 1f074305f1..86617e0aa7 100644
--- a/runtime/autoload/python3complete.vim
+++ b/runtime/autoload/python3complete.vim
@@ -135,6 +135,9 @@ class Completer(object):
        self.parser = PyParser()
 
     def evalsource(self,text,line=0):
+        # vim is imported locally in vimpy3complete(); re-import here so the
+        # vim.eval() below works (otherwise NameError, silently caught).
+        import vim
         sc = self.parser.parse(text,line)
         try: allow_imports = int(
           vim.eval("get(g:, 'pythoncomplete_allow_import', 0)"))
diff --git a/runtime/autoload/pythoncomplete.vim b/runtime/autoload/pythoncomplete.vim
index e9fd9dc490..eb87bd6c0f 100644
--- a/runtime/autoload/pythoncomplete.vim
+++ b/runtime/autoload/pythoncomplete.vim
@@ -149,6 +149,9 @@ class Completer(object):
        self.parser = PyParser()
 
     def evalsource(self,text,line=0):
+        # vim is imported locally in vimcomplete(); re-import here so the
+        # vim.eval() below works (otherwise NameError, silently caught).
+        import vim
         sc = self.parser.parse(text,line)
         try: allow_imports = int(
           vim.eval("get(g:, 'pythoncomplete_allow_import', 0)"))
diff --git a/test/old/testdir/test_popup.vim b/test/old/testdir/test_popup.vim
index 07e3d8540b..633b45a506 100644
--- a/test/old/testdir/test_popup.vim
+++ b/test/old/testdir/test_popup.vim
@@ -725,6 +725,9 @@ func Test_popup_and_preview_autocommand()
     au!
     au BufAdd * nested tab sball
   augroup END
+  " Let pythoncomplete follow the buffer's 'import os' (off by default
+  " since v9.2.0561) so 'os.' can be completed.
+  let g:pythoncomplete_allow_import = 1
   set omnifunc=pythoncomplete#Complete
   call setline(1, 'import os')
   " make the line long
@@ -747,6 +750,7 @@ func Test_popup_and_preview_autocommand()
   augroup END
   augroup! MyBufAdd
   bw!
+  unlet g:pythoncomplete_allow_import
 endfunc
 
 func s:run_popup_and_previewwindow_dump(lines, dumpfile)