diff --git a/Doc/library/mmap.rst b/Doc/library/mmap.rst
index 128bc90259c8..7a901c93f7e0 100644
--- a/Doc/library/mmap.rst
+++ b/Doc/library/mmap.rst
@@ -86,6 +86,10 @@ To map anonymous memory, -1 should be passed as the fileno along with the length
    defaults to 0.  *offset* must be a multiple of the PAGESIZE or
    ALLOCATIONGRANULARITY.
 
+   To ensure validity of the created memory mapping the file specified
+   by the descriptor *fileno* is internally automatically synchronized
+   with physical backing store on Mac OS X and OpenVMS.
+
    This example shows a simple way of using :class:`mmap`::
 
       import mmap
diff --git a/Lib/test/test_zlib.py b/Lib/test/test_zlib.py
index 5d38d97836af..9aafffa8d21a 100644
--- a/Lib/test/test_zlib.py
+++ b/Lib/test/test_zlib.py
@@ -70,7 +70,7 @@ def setUp(self):
         with open(support.TESTFN, "wb+") as f:
             f.seek(_4G)
             f.write(b"asdf")
-        with open(support.TESTFN, "rb") as f:
+            f.flush()
             self.mapping = mmap.mmap(f.fileno(), 0, access=mmap.ACCESS_READ)
 
     def tearDown(self):
diff --git a/Misc/NEWS b/Misc/NEWS
index 592223348ce1..2a500949bc18 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -79,6 +79,9 @@ Core and Builtins
 Library
 -------
 
+- Issue #11277: mmap.mmap() calls fcntl(fd, F_FULLFSYNC) on Mac OS X to get
+  around a mmap bug with sparse files. Patch written by Steffen Daode Nurpmeso.
+
 - Issue #11858: configparser.ExtendedInterpolation expected lower-case section
   names.
 
diff --git a/Modules/mmapmodule.c b/Modules/mmapmodule.c
index fdf39223567a..36ca67d3c145 100644
--- a/Modules/mmapmodule.c
+++ b/Modules/mmapmodule.c
@@ -23,6 +23,9 @@
 
 #ifndef MS_WINDOWS
 #define UNIX
+# ifdef __APPLE__
+#  include <fcntl.h>
+# endif
 #endif
 
 #ifdef MS_WINDOWS
@@ -1122,6 +1125,12 @@ new_mmap_object(PyTypeObject *type, PyObject *args, PyObject *kwdict)
                             "mmap invalid access parameter.");
     }
 
+#ifdef __APPLE__
+    /* Issue #11277: fsync(2) is not enough on OS X - a special, OS X specific
+       fcntl(2) is necessary to force DISKSYNC and get around mmap(2) bug */
+    if (fd != -1)
+        (void)fcntl(fd, F_FULLFSYNC);
+#endif
 #ifdef HAVE_FSTAT
 #  ifdef __VMS
     /* on OpenVMS we must ensure that all bytes are written to the file */