diff --git a/Lib/tarfile.py b/Lib/tarfile.py
index e3747e9..0f9d1da 100644
--- a/Lib/tarfile.py
+++ b/Lib/tarfile.py
@@ -760,9 +760,8 @@
                         self.map_index = 0
             length = min(size, stop - self.position)
             if data:
-                self.fileobj.seek(offset)
-                block = self.fileobj.read(stop - start)
-                buf += block[self.position - start:self.position + length]
+                self.fileobj.seek(offset + (self.position - start))
+                buf += self.fileobj.read(length)
             else:
                 buf += NUL * length
             size -= length
diff --git a/Lib/test/test_tarfile.py b/Lib/test/test_tarfile.py
index 94ef61c..68e094d 100644
--- a/Lib/test/test_tarfile.py
+++ b/Lib/test/test_tarfile.py
@@ -419,6 +419,22 @@
 
     mode="r|"
 
+    def test_read_through(self):
+        # Issue #11224: A poorly designed _FileInFile.read() method
+        # caused seeking errors with stream tar files.
+        for tarinfo in self.tar:
+            if not tarinfo.isreg():
+                continue
+            fobj = self.tar.extractfile(tarinfo)
+            while True:
+                try:
+                    buf = fobj.read(512)
+                except tarfile.StreamError:
+                    self.fail("simple read-through using TarFile.extractfile() failed")
+                if not buf:
+                    break
+            fobj.close()
+
     def test_fileobj_regular_file(self):
         tarinfo = self.tar.next() # get "regtype" (can't use getmember)
         fobj = self.tar.extractfile(tarinfo)
diff --git a/Misc/NEWS b/Misc/NEWS
index a3a246c..9dcd309 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -27,6 +27,10 @@
 Library
 -------
 
+- Issue #11224: Fixed a regression in tarfile that affected the file-like
+  objects returned by TarFile.extractfile() regarding performance, memory
+  consumption and failures with the stream interface.
+
 - Issue #10924: Adding salt and Modular Crypt Format to crypt library.
   Moved old C wrapper to _crypt, and added a Python wrapper with
   enhanced salt generation and simpler API for password generation.