diff --git a/Lib/test/test_hashlib.py b/Lib/test/test_hashlib.py
index f0e2d527af2615..b4861366b11162 100644
--- a/Lib/test/test_hashlib.py
+++ b/Lib/test/test_hashlib.py
@@ -16,14 +16,16 @@
 import sys
 import sysconfig
 import tempfile
+import textwrap
 import threading
 import unittest
 from test import support
 from test.support import _4G, bigmemtest
 from test.support import hashlib_helper
-from test.support.import_helper import import_fresh_module
+from test.support import import_helper
 from test.support import requires_resource
 from test.support import threading_helper
+from test.support.script_helper import assert_python_ok
 from http.client import HTTPException
 
 
@@ -37,7 +39,7 @@
     builtin_hashes = set(map(str.strip, builtin_hash_names))
 
 # Public 'hashlib' module with OpenSSL backend for PBKDF2.
-openssl_hashlib = import_fresh_module('hashlib', fresh=['_hashlib'])
+openssl_hashlib = import_helper.import_fresh_module('hashlib', fresh=['_hashlib'])
 
 try:
     import _hashlib
@@ -1201,6 +1203,22 @@ def test_readonly_types(self):
                     with self.assertRaisesRegex(TypeError, "immutable type"):
                         hash_type.value = False
 
+    @unittest.skipUnless(HASH is not None, 'need _hashlib')
+    def test_hashlib_init_memory_error_no_df(self):
+        """gh-145301 regression test."""
+        import_helper.import_module('_testcapi')
+        code = textwrap.dedent("""
+            import _testcapi
+            _testcapi.set_nomemory(40, 41)
+            try:
+                import _hashlib
+            except (MemoryError, ImportError):
+                pass
+            finally:
+                _testcapi.remove_mem_hooks()
+        """)
+        assert_python_ok('-c', code)
+
 
 class KDFTests(unittest.TestCase):
 
diff --git a/Misc/NEWS.d/next/Library/2026-02-27-19-00-26.gh-issue-145301.2Wih4b.rst b/Misc/NEWS.d/next/Library/2026-02-27-19-00-26.gh-issue-145301.2Wih4b.rst
new file mode 100644
index 00000000000000..7aeb6a1145ab4c
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2026-02-27-19-00-26.gh-issue-145301.2Wih4b.rst
@@ -0,0 +1,2 @@
+:mod:`hashlib`: fix a crash when the initialization of the underlying C
+extension module fails.
diff --git a/Misc/NEWS.d/next/Library/2026-02-28-00-55-00.gh-issue-145301.Lk2bRl.rst b/Misc/NEWS.d/next/Library/2026-02-28-00-55-00.gh-issue-145301.Lk2bRl.rst
new file mode 100644
index 00000000000000..436ff316b2c327
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2026-02-28-00-55-00.gh-issue-145301.Lk2bRl.rst
@@ -0,0 +1,2 @@
+:mod:`hmac`: fix a crash when the initialization of the underlying C
+extension module fails.
diff --git a/Modules/_hashopenssl.c b/Modules/_hashopenssl.c
index 77832a768e0cbc..e19eb1abcf2c4d 100644
--- a/Modules/_hashopenssl.c
+++ b/Modules/_hashopenssl.c
@@ -268,7 +268,7 @@ py_hashentry_table_new(void) {
 
         if (h->py_alias != NULL) {
             if (_Py_hashtable_set(ht, (const void*)entry->py_alias, (void*)entry) < 0) {
-                PyMem_Free(entry);
+                /* entry is already in ht, will be freed by _Py_hashtable_destroy() */
                 goto error;
             }
             entry->refcnt++;
diff --git a/Modules/hmacmodule.c b/Modules/hmacmodule.c
index f074f24807703c..a61b03c533ba3b 100644
--- a/Modules/hmacmodule.c
+++ b/Modules/hmacmodule.c
@@ -1453,16 +1453,19 @@ py_hmac_hinfo_ht_new(void)
         assert(value->display_name == NULL);
         value->refcnt = 0;
 
-#define Py_HMAC_HINFO_LINK(KEY)                                 \
-        do {                                                    \
-            int rc = py_hmac_hinfo_ht_add(table, KEY, value);   \
-            if (rc < 0) {                                       \
-                PyMem_Free(value);                              \
-                goto error;                                     \
-            }                                                   \
-            else if (rc == 1) {                                 \
-                value->refcnt++;                                \
-            }                                                   \
+#define Py_HMAC_HINFO_LINK(KEY)                                    \
+        do {                                                       \
+            int rc = py_hmac_hinfo_ht_add(table, KEY, value);      \
+            if (rc < 0) {                                          \
+                /* entry may already be in ht, freed upon exit */  \
+                if (value->refcnt == 0) {                          \
+                    PyMem_Free(value);                             \
+                }                                                  \
+                goto error;                                        \
+            }                                                      \
+            else if (rc == 1) {                                    \
+                value->refcnt++;                                   \
+            }                                                      \
         } while (0)
         Py_HMAC_HINFO_LINK(e->name);
         Py_HMAC_HINFO_LINK(e->hashlib_name);