diff --git a/Lib/email/feedparser.py b/Lib/email/feedparser.py
index 7c07ca86457a2a..8e945ac26bf169 100644
--- a/Lib/email/feedparser.py
+++ b/Lib/email/feedparser.py
@@ -189,6 +189,7 @@ def close(self):
         assert not self._msgstack
         # Look for final set of defects
         if root.get_content_maintype() == 'multipart' \
+               and not self._headersonly \
                and not root.is_multipart():
             defect = errors.MultipartInvariantViolationDefect()
             self.policy.handle_defect(root, defect)
diff --git a/Lib/http/client.py b/Lib/http/client.py
index 5aa178d7b127d9..74825ba0b99540 100644
--- a/Lib/http/client.py
+++ b/Lib/http/client.py
@@ -211,7 +211,7 @@ def parse_headers(fp, _class=HTTPMessage):
         if line in (b'\r\n', b'\n', b''):
             break
     hstring = b''.join(headers).decode('iso-8859-1')
-    return email.parser.Parser(_class=_class).parsestr(hstring)
+    return email.parser.Parser(_class=_class).parsestr(hstring, headersonly=True)
 
 
 class HTTPResponse(io.BufferedIOBase):
diff --git a/Lib/test/test_email/test_parser.py b/Lib/test/test_email/test_parser.py
index 06c86408ab52b9..45a6d861580a94 100644
--- a/Lib/test/test_email/test_parser.py
+++ b/Lib/test/test_email/test_parser.py
@@ -5,6 +5,12 @@
 from email.policy import default
 from test.test_email import TestEmailBase
 
+class TestFeedParser(TestEmailBase):
+    def test_multipart_message_with_headers_only(self):
+        import email.parser
+        header = 'Content-Type: multipart/related; boundary="==="\r\n\r\n'
+        msg = email.parser.Parser().parsestr(header, headersonly=True)
+        self.assertDefectsEqual(msg.defects, [])
 
 class TestCustomMessage(TestEmailBase):
 
diff --git a/Lib/test/test_httplib.py b/Lib/test/test_httplib.py
index f816eac83b682d..7c7446c42ac8fc 100644
--- a/Lib/test/test_httplib.py
+++ b/Lib/test/test_httplib.py
@@ -359,6 +359,11 @@ def test_headers_debuglevel(self):
         self.assertEqual(lines[1], "header: First: val")
         self.assertEqual(lines[2], "header: Second: val")
 
+    def test_parse_valid_multipart_header(self):
+        header = b'Content-Type: multipart/related; boundary="==="\r\n\r\n'
+        fp = io.BytesIO(header)
+        message = client.parse_headers(fp)
+        self.assertListEqual(message.defects, [])
 
 class TransferEncodingTest(TestCase):
     expected_body = b"It's just a flesh wound"
diff --git a/Misc/NEWS.d/next/Library/2019-09-05-12-13-11.bpo-36226.J5mcDO.rst b/Misc/NEWS.d/next/Library/2019-09-05-12-13-11.bpo-36226.J5mcDO.rst
new file mode 100644
index 00000000000000..7ab68b926cc83d
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2019-09-05-12-13-11.bpo-36226.J5mcDO.rst
@@ -0,0 +1,2 @@
+Fixes false MultipartInvariantViolationDefects which were triggered when
+only headers of a multipart message were parsed.
diff --git a/Misc/NEWS.d/next/Library/2019-09-05-12-14-30.bpo-36226.KJV4rP.rst b/Misc/NEWS.d/next/Library/2019-09-05-12-14-30.bpo-36226.KJV4rP.rst
new file mode 100644
index 00000000000000..98270ea2dba595
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2019-09-05-12-14-30.bpo-36226.KJV4rP.rst
@@ -0,0 +1,2 @@
+Fixes false StartBoundaryNotFoundDefects which were triggered by
+parse_headers not forwarding the headersonly to the email parser.