diff --git a/Lib/annotationlib.py b/Lib/annotationlib.py
index 5ad0893106a72b..c0b1d4395d14ed 100644
--- a/Lib/annotationlib.py
+++ b/Lib/annotationlib.py
@@ -868,7 +868,7 @@ def get_annotations(
             # For FORWARDREF, we use __annotations__ if it exists
             try:
                 ann = _get_dunder_annotations(obj)
-            except NameError:
+            except Exception:
                 pass
             else:
                 if ann is not None:
diff --git a/Lib/dataclasses.py b/Lib/dataclasses.py
index 0f7dc9ae6b82f5..86d29df0639184 100644
--- a/Lib/dataclasses.py
+++ b/Lib/dataclasses.py
@@ -244,6 +244,10 @@ def __repr__(self):
     property,
 })
 
+# Any marker is used in `make_dataclass` to mark unannotated fields as `Any`
+# without importing `typing` module.
+_ANY_MARKER = object()
+
 
 class InitVar:
     __slots__ = ('type', )
@@ -1591,7 +1595,7 @@ class C(Base):
     for item in fields:
         if isinstance(item, str):
             name = item
-            tp = 'typing.Any'
+            tp = _ANY_MARKER
         elif len(item) == 2:
             name, tp, = item
         elif len(item) == 3:
@@ -1610,15 +1614,49 @@ class C(Base):
         seen.add(name)
         annotations[name] = tp
 
+    # We initially block the VALUE format, because inside dataclass() we'll
+    # call get_annotations(), which will try the VALUE format first. If we don't
+    # block, that means we'd always end up eagerly importing typing here, which
+    # is what we're trying to avoid.
+    value_blocked = True
+
+    def annotate_method(format):
+        def get_any():
+            match format:
+                case annotationlib.Format.STRING:
+                    return 'typing.Any'
+                case annotationlib.Format.FORWARDREF:
+                    typing = sys.modules.get("typing")
+                    if typing is None:
+                        return annotationlib.ForwardRef("Any", module="typing")
+                    else:
+                        return typing.Any
+                case annotationlib.Format.VALUE:
+                    if value_blocked:
+                        raise NotImplementedError
+                    from typing import Any
+                    return Any
+                case _:
+                    raise NotImplementedError
+        annos = {
+            ann: get_any() if t is _ANY_MARKER else t
+            for ann, t in annotations.items()
+        }
+        if format == annotationlib.Format.STRING:
+            return annotationlib.annotations_to_string(annos)
+        else:
+            return annos
+
     # Update 'ns' with the user-supplied namespace plus our calculated values.
     def exec_body_callback(ns):
         ns.update(namespace)
         ns.update(defaults)
-        ns['__annotations__'] = annotations
 
     # We use `types.new_class()` instead of simply `type()` to allow dynamic creation
     # of generic dataclasses.
     cls = types.new_class(cls_name, bases, {}, exec_body_callback)
+    # For now, set annotations including the _ANY_MARKER.
+    cls.__annotate__ = annotate_method
 
     # For pickling to work, the __module__ variable needs to be set to the frame
     # where the dataclass is created.
@@ -1634,10 +1672,13 @@ def exec_body_callback(ns):
         cls.__module__ = module
 
     # Apply the normal provided decorator.
-    return decorator(cls, init=init, repr=repr, eq=eq, order=order,
-                     unsafe_hash=unsafe_hash, frozen=frozen,
-                     match_args=match_args, kw_only=kw_only, slots=slots,
-                     weakref_slot=weakref_slot)
+    cls = decorator(cls, init=init, repr=repr, eq=eq, order=order,
+                    unsafe_hash=unsafe_hash, frozen=frozen,
+                    match_args=match_args, kw_only=kw_only, slots=slots,
+                    weakref_slot=weakref_slot)
+    # Now that the class is ready, allow the VALUE format.
+    value_blocked = False
+    return cls
 
 
 def replace(obj, /, **changes):
diff --git a/Lib/test/test_dataclasses/__init__.py b/Lib/test/test_dataclasses/__init__.py
index 99fefb57fd0f09..ac78f8327b808e 100644
--- a/Lib/test/test_dataclasses/__init__.py
+++ b/Lib/test/test_dataclasses/__init__.py
@@ -5,6 +5,7 @@
 from dataclasses import *
 
 import abc
+import annotationlib
 import io
 import pickle
 import inspect
@@ -12,6 +13,7 @@
 import types
 import weakref
 import traceback
+import sys
 import textwrap
 import unittest
 from unittest.mock import Mock
@@ -25,6 +27,7 @@
 import dataclasses  # Needed for the string "dataclasses.InitVar[int]" to work as an annotation.
 
 from test import support
+from test.support import import_helper
 
 # Just any custom exception we can catch.
 class CustomError(Exception): pass
@@ -3754,7 +3757,6 @@ class A(WithDictSlot): ...
     @support.cpython_only
     def test_dataclass_slot_dict_ctype(self):
         # https://github.com/python/cpython/issues/123935
-        from test.support import import_helper
         # Skips test if `_testcapi` is not present:
         _testcapi = import_helper.import_module('_testcapi')
 
@@ -4246,16 +4248,56 @@ def test_no_types(self):
         C = make_dataclass('Point', ['x', 'y', 'z'])
         c = C(1, 2, 3)
         self.assertEqual(vars(c), {'x': 1, 'y': 2, 'z': 3})
-        self.assertEqual(C.__annotations__, {'x': 'typing.Any',
-                                             'y': 'typing.Any',
-                                             'z': 'typing.Any'})
+        self.assertEqual(C.__annotations__, {'x': typing.Any,
+                                             'y': typing.Any,
+                                             'z': typing.Any})
 
         C = make_dataclass('Point', ['x', ('y', int), 'z'])
         c = C(1, 2, 3)
         self.assertEqual(vars(c), {'x': 1, 'y': 2, 'z': 3})
-        self.assertEqual(C.__annotations__, {'x': 'typing.Any',
+        self.assertEqual(C.__annotations__, {'x': typing.Any,
                                              'y': int,
-                                             'z': 'typing.Any'})
+                                             'z': typing.Any})
+
+    def test_no_types_get_annotations(self):
+        C = make_dataclass('C', ['x', ('y', int), 'z'])
+
+        self.assertEqual(
+            annotationlib.get_annotations(C, format=annotationlib.Format.VALUE),
+            {'x': typing.Any, 'y': int, 'z': typing.Any},
+        )
+        self.assertEqual(
+            annotationlib.get_annotations(
+                C, format=annotationlib.Format.FORWARDREF),
+            {'x': typing.Any, 'y': int, 'z': typing.Any},
+        )
+        self.assertEqual(
+            annotationlib.get_annotations(
+                C, format=annotationlib.Format.STRING),
+            {'x': 'typing.Any', 'y': 'int', 'z': 'typing.Any'},
+        )
+
+    def test_no_types_no_typing_import(self):
+        with import_helper.CleanImport('typing'):
+            self.assertNotIn('typing', sys.modules)
+            C = make_dataclass('C', ['x', ('y', int)])
+
+            self.assertNotIn('typing', sys.modules)
+            self.assertEqual(
+                C.__annotate__(annotationlib.Format.FORWARDREF),
+                {
+                    'x': annotationlib.ForwardRef('Any', module='typing'),
+                    'y': int,
+                },
+            )
+            self.assertNotIn('typing', sys.modules)
+
+            for field in fields(C):
+                if field.name == "x":
+                    self.assertEqual(field.type, annotationlib.ForwardRef('Any', module='typing'))
+                else:
+                    self.assertEqual(field.name, "y")
+                    self.assertIs(field.type, int)
 
     def test_module_attr(self):
         self.assertEqual(ByMakeDataClass.__module__, __name__)
diff --git a/Misc/NEWS.d/next/Library/2024-09-18-09-15-40.gh-issue-82129.GQwt3u.rst b/Misc/NEWS.d/next/Library/2024-09-18-09-15-40.gh-issue-82129.GQwt3u.rst
new file mode 100644
index 00000000000000..b8661f9eeaa5c9
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2024-09-18-09-15-40.gh-issue-82129.GQwt3u.rst
@@ -0,0 +1,2 @@
+Fix :exc:`NameError` when calling :func:`typing.get_type_hints` on a :func:`dataclasses.dataclass` created by
+:func:`dataclasses.make_dataclass` with un-annotated fields.