diff --git a/python/src/com/jetbrains/python/psi/resolve/VariantsProcessor.java b/python/src/com/jetbrains/python/psi/resolve/VariantsProcessor.java
index 392b014d48e7..4246bd0aaa4f 100644
--- a/python/src/com/jetbrains/python/psi/resolve/VariantsProcessor.java
+++ b/python/src/com/jetbrains/python/psi/resolve/VariantsProcessor.java
@@ -77,7 +77,7 @@ public abstract class VariantsProcessor implements PsiScopeProcessor {
         final NameDefiner definer = (NameDefiner)element;
         for (PyElement expr : definer.iterateNames()) {
           if (expr != null && expr != myContext) { // NOTE: maybe rather have SingleIterables skip nulls outright?
-            String referencedName = expr.getName();
+            String referencedName = expr instanceof PyFile ? FileUtil.getNameWithoutExtension(((PyFile) expr).getName()) : expr.getName();
             if (referencedName != null && nameIsAcceptable(referencedName)) {
               addImportedElement(referencedName, definer, expr);
             }
diff --git a/python/testData/completion/moduleDotPy/a.after.py b/python/testData/completion/moduleDotPy/a.after.py
new file mode 100644
index 000000000000..5df601b2022f
--- /dev/null
+++ b/python/testData/completion/moduleDotPy/a.after.py
@@ -0,0 +1,3 @@
+from shazam import *
+
+xyzzy
\ No newline at end of file
diff --git a/python/testData/completion/moduleDotPy/a.py b/python/testData/completion/moduleDotPy/a.py
new file mode 100644
index 000000000000..574af1da8125
--- /dev/null
+++ b/python/testData/completion/moduleDotPy/a.py
@@ -0,0 +1,3 @@
+from shazam import *
+
+xy<caret>
\ No newline at end of file
diff --git a/python/testData/completion/moduleDotPy/shazam.py b/python/testData/completion/moduleDotPy/shazam.py
new file mode 100644
index 000000000000..81a82a11778e
--- /dev/null
+++ b/python/testData/completion/moduleDotPy/shazam.py
@@ -0,0 +1 @@
+import xyzzy
diff --git a/python/testData/completion/moduleDotPy/xyzzy.py b/python/testData/completion/moduleDotPy/xyzzy.py
new file mode 100644
index 000000000000..e69de29bb2d1
diff --git a/python/testSrc/com/jetbrains/python/PythonCompletionTest.java b/python/testSrc/com/jetbrains/python/PythonCompletionTest.java
index 110f359fabfe..92a4a2599df7 100644
--- a/python/testSrc/com/jetbrains/python/PythonCompletionTest.java
+++ b/python/testSrc/com/jetbrains/python/PythonCompletionTest.java
@@ -387,6 +387,10 @@ public class PythonCompletionTest extends PyTestCase {
     doMultiFileTest();
   }
 
+  public void testModuleDotPy() {  // PY-5813
+    doMultiFileTest();
+  }
+
   public void testHasAttr() {  // PY-4423
     doTest();
   }