diff --git a/Lib/dataclasses.py b/Lib/dataclasses.py
index a567a33d646f44..a9c4d433ba2a8e 100644
--- a/Lib/dataclasses.py
+++ b/Lib/dataclasses.py
@@ -605,16 +605,25 @@ def _frozen_get_del_attr(cls, fields, globals):
     else:
         # Special case for the zero-length tuple.
         fields_str = '()'
+
+    # bpo-45897: Do not raise FrozenInstanceError
+    # if the dataclass has slots & the attribute is not specified in __slots__.
+    # Instead, let the standard __slots__ machinery raise AttributeError naturally
+    # in the super(cls, self).__setattr__ call
     return (_create_fn('__setattr__',
                       ('self', 'name', 'value'),
-                      (f'if type(self) is cls or name in {fields_str}:',
+                      (f'if "__slots__" in cls.__dict__ and name not in cls.__slots__:',
+                        ' pass',
+                       f'elif type(self) is cls or name in {fields_str}:',
                         ' raise FrozenInstanceError(f"cannot assign to field {name!r}")',
                        f'super(cls, self).__setattr__(name, value)'),
                        locals=locals,
                        globals=globals),
             _create_fn('__delattr__',
                       ('self', 'name'),
-                      (f'if type(self) is cls or name in {fields_str}:',
+                      (f'if "__slots__" in cls.__dict__ and name not in cls.__slots__:',
+                        ' pass',
+                       f'elif type(self) is cls or name in {fields_str}:',
                         ' raise FrozenInstanceError(f"cannot delete field {name!r}")',
                        f'super(cls, self).__delattr__(name)'),
                        locals=locals,
@@ -1075,12 +1084,6 @@ def _process_class(cls, init, repr, eq, order, unsafe_hash, frozen,
                                 f'in class {cls.__name__}. Consider using '
                                 'functools.total_ordering')
 
-    if frozen:
-        for fn in _frozen_get_del_attr(cls, field_list, globals):
-            if _set_new_attribute(cls, fn.__name__, fn):
-                raise TypeError(f'Cannot overwrite attribute {fn.__name__} '
-                                f'in class {cls.__name__}')
-
     # Decide if/how we're going to create a hash function.
     hash_action = _hash_action[bool(unsafe_hash),
                                bool(eq),
@@ -1107,6 +1110,14 @@ def _process_class(cls, init, repr, eq, order, unsafe_hash, frozen,
     if slots:
         cls = _add_slots(cls, frozen, weakref_slot)
 
+    # Frozen __setattr__/__delattr__ must be added after __slots__
+    # bpo-45897
+    if frozen:
+        for fn in _frozen_get_del_attr(cls, field_list, globals):
+            if _set_new_attribute(cls, fn.__name__, fn):
+                raise TypeError(f'Cannot overwrite attribute {fn.__name__} '
+                                f'in class {cls.__name__}')
+
     abc.update_abstractmethods(cls)
 
     return cls
diff --git a/Lib/test/test_dataclasses.py b/Lib/test/test_dataclasses.py
index e2eab695789de7..b120fbb2e36285 100644
--- a/Lib/test/test_dataclasses.py
+++ b/Lib/test/test_dataclasses.py
@@ -3039,6 +3039,63 @@ class A:
         self.assertEqual(obj.a, 'a')
         self.assertEqual(obj.b, 'b')
 
+    def test_frozen_slots_raises_correct_error(self):
+        # bpo-45897: for a frozen-slotted dataclass instance, attempting to set
+        # an attribute not specified in __slots__ should raise AttributeError,
+        # not TypeError or FrozenInstanceError
+        @dataclass(slots=True, frozen=True)
+        class Point:
+            x: int
+            y: int
+
+        p = Point(1, 2)
+        self.assertEqual(p.x, 1)
+        self.assertEqual(p.y, 2)
+        with self.assertRaises(FrozenInstanceError):
+            p.x = 2
+
+        regex = 'object has no attribute'
+        with self.assertRaisesRegex(AttributeError, regex) as ex:
+            p.z = 5
+        type_of_caught_exception = type(ex.exception)
+
+        # Verify that the caught exception is `AttributeError` exactly,
+        # and *not* a subclass of `AttributeError` such as `FrozenInstanceError`.
+        #
+        # We need to ensure that this error is being caused by the standard machinery that
+        # prevents new attributes being added that aren't specified in __slots__.
+        #
+        # We *do not* want the error to be caused by anything related to dataclasses.
+        self.assertIs(
+            type_of_caught_exception,
+            AttributeError,
+            msg=f"expected 'AttributeError', got {type_of_caught_exception.__name__!r}"
+        )
+
+        @dataclass(frozen=True)
+        class DataclassSubclassOfPointWithNoSlots(Point): pass
+
+        d = DataclassSubclassOfPointWithNoSlots(1, 2)
+        with self.assertRaises(FrozenInstanceError):
+            d.x = 2
+
+        # The subclass is frozen, so any attempt to set an attribute should
+        # raise an error. The subclass does not define slots, however, so the
+        # error should be `FrozenInstanceError` here rather than
+        # `AttributeError`.
+        with self.assertRaises(FrozenInstanceError):
+            d.z = 5
+
+        class NonDataclassSubclassOfPointWithNoSlots(Point): pass
+
+        n = NonDataclassSubclassOfPointWithNoSlots(1, 2)
+        with self.assertRaises(FrozenInstanceError):
+            n.x = 2
+
+        # This should pass without any exception being raised, since the
+        # subclass does not define __slots__ and is not frozen.
+        n.z = 5
+
     def test_slots_no_weakref(self):
         @dataclass(slots=True)
         class A:
diff --git a/Misc/NEWS.d/next/Library/2021-12-01-21-45-43.bpo-45897.lAZPRy.rst b/Misc/NEWS.d/next/Library/2021-12-01-21-45-43.bpo-45897.lAZPRy.rst
new file mode 100644
index 00000000000000..7f873b7f8899ab
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2021-12-01-21-45-43.bpo-45897.lAZPRy.rst
@@ -0,0 +1,4 @@
+Fix bug in dataclasses where a frozen dataclass with slots would raise
+``TypeError`` rather than ``AttributeError`` if a user attempted to
+set/delete an attribute that was not specified in ``__slots__``. Patch by
+Alex Waygood.