diff --git a/django/middleware/gzip.py b/django/middleware/gzip.py
index 7ccd00ac19..eb151d7ad5 100644
--- a/django/middleware/gzip.py
+++ b/django/middleware/gzip.py
@@ -1,7 +1,7 @@
 from django.utils.cache import patch_vary_headers
 from django.utils.deprecation import MiddlewareMixin
 from django.utils.regex_helper import _lazy_re_compile
-from django.utils.text import compress_sequence, compress_string
+from django.utils.text import acompress_sequence, compress_sequence, compress_string
 
 re_accepts_gzip = _lazy_re_compile(r"\bgzip\b")
 
@@ -32,18 +32,10 @@ class GZipMiddleware(MiddlewareMixin):
 
         if response.streaming:
             if response.is_async:
-                # pull to lexical scope to capture fixed reference in case
-                # streaming_content is set again later.
-                original_iterator = response.streaming_content
-
-                async def gzip_wrapper():
-                    async for chunk in original_iterator:
-                        yield compress_string(
-                            chunk,
-                            max_random_bytes=self.max_random_bytes,
-                        )
-
-                response.streaming_content = gzip_wrapper()
+                response.streaming_content = acompress_sequence(
+                    response.streaming_content,
+                    max_random_bytes=self.max_random_bytes,
+                )
             else:
                 response.streaming_content = compress_sequence(
                     response.streaming_content,
diff --git a/django/utils/text.py b/django/utils/text.py
index 26edde99e3..bad1da6729 100644
--- a/django/utils/text.py
+++ b/django/utils/text.py
@@ -393,6 +393,22 @@ def compress_sequence(sequence, *, max_random_bytes=None):
     yield buf.read()
 
 
+async def acompress_sequence(sequence, *, max_random_bytes=None):
+    buf = StreamingBuffer()
+    filename = _get_random_filename(max_random_bytes) if max_random_bytes else None
+    with GzipFile(
+        filename=filename, mode="wb", compresslevel=6, fileobj=buf, mtime=0
+    ) as zfile:
+        # Output headers...
+        yield buf.read()
+        async for item in sequence:
+            zfile.write(item)
+            data = buf.read()
+            if data:
+                yield data
+    yield buf.read()
+
+
 # Expression to match some_token and some_token="with spaces" (and similarly
 # for single-quoted strings).
 smart_split_re = _lazy_re_compile(
diff --git a/tests/middleware/tests.py b/tests/middleware/tests.py
index c4aac0552b..a61c4b147f 100644
--- a/tests/middleware/tests.py
+++ b/tests/middleware/tests.py
@@ -2,6 +2,7 @@ import gzip
 import random
 import re
 import struct
+import zlib
 from io import BytesIO
 from unittest import mock
 from urllib.parse import quote
@@ -880,8 +881,8 @@ class GZipMiddlewareTest(SimpleTestCase):
 
     @staticmethod
     def decompress(gzipped_string):
-        with gzip.GzipFile(mode="rb", fileobj=BytesIO(gzipped_string)) as f:
-            return f.read()
+        # Use zlib to ensure gzipped_string contains exactly one gzip stream.
+        return zlib.decompress(gzipped_string, zlib.MAX_WBITS | 16)
 
     @staticmethod
     def get_mtime(gzipped_string):