diff --git a/jsonschema/_keywords.py b/jsonschema/_keywords.py
index f30f95419..786d0e2e5 100644
--- a/jsonschema/_keywords.py
+++ b/jsonschema/_keywords.py
@@ -1,5 +1,8 @@
+from __future__ import annotations
+
 from fractions import Fraction
 import re
+import typing
 
 from jsonschema._utils import (
     ensure_list,
@@ -13,6 +16,58 @@
 from jsonschema.exceptions import FormatError, ValidationError
 
 
+class Keyword:
+    """
+    The Keyword wraps a function to maintain full back-compatibility.
+
+    The class adds the ability to annotate the keyword implementation while
+    behaving like a function, i.e. `Keyword(func)` behaves like `func` itself
+    in most cases, and allows a more formal description of the behavior and
+    dependencies.
+    """
+
+    def __init__(
+            self,
+            func: typing.Optional[typing.Callable] = None, /,
+            needs: typing.Optional[typing.Iterable[str]] = (),
+    ):
+        self.func = func
+        self.needs = needs
+
+    def __call__(self, validator, property, instance, schema):
+        if self.func is None:
+            raise NotImplementedError(f"{self} has no validation method.")
+        return self.func(validator, property, instance, schema)
+
+
+def keyword(func: typing.Optional[typing.Callable] = None, /, **kwargs):
+    """
+    Syntactic sugar to decorate a function as a keyword.
+
+    The function is not modified, but wrapped by a Keyword object. This allows
+    the same function to be reused as by multiple validators with different
+    annotations.
+
+    Examples
+    --------
+    Functionally equivalent to the un-decorated function.
+    >>> @keyword
+    ... def myKeyword(validator, property, instance, schema):
+    ...     ...
+
+    Mark the keyword "else" to be evaluated after "if"
+    >>> @keyword(needs=["if"])
+    ... def else_(validator, property, instance, schema):
+    ...     ...
+
+    >>> kw = keyword(else_, needs="if")
+
+    """
+    if func is None:
+        return lambda fun: Keyword(fun, **kwargs)
+    return Keyword(func, **kwargs)
+
+
 def patternProperties(validator, patternProperties, instance, schema):
     if not validator.is_type(instance, "object"):
         return
@@ -389,6 +444,21 @@ def if_(validator, if_schema, instance, schema):
         yield from validator.descend(instance, else_, schema_path="else")
 
 
+@keyword(
+    needs=[
+        "prefixItems",
+        "items",
+        "contains",
+        "allOf",
+        "anyOf",
+        "oneOf",
+        "not",
+        "if",
+        "then",
+        "else",
+        "dependentSchemas",
+    ],
+)
 def unevaluatedItems(validator, unevaluatedItems, instance, schema):
     if not validator.is_type(instance, "array"):
         return
@@ -404,6 +474,21 @@ def unevaluatedItems(validator, unevaluatedItems, instance, schema):
         yield ValidationError(error % extras_msg(unevaluated_items))
 
 
+@keyword(
+    needs=[
+        "properties",
+        "patternProperties",
+        "additionalProperties",
+        "allOf",
+        "anyOf",
+        "oneOf",
+        "not",
+        "if",
+        "then",
+        "else",
+        "dependentSchemas",
+    ],
+)
 def unevaluatedProperties(validator, unevaluatedProperties, instance, schema):
     if not validator.is_type(instance, "object"):
         return
diff --git a/jsonschema/tests/test_validators.py b/jsonschema/tests/test_validators.py
index 28cc40273..11d545197 100644
--- a/jsonschema/tests/test_validators.py
+++ b/jsonschema/tests/test_validators.py
@@ -742,6 +742,35 @@ def test_unevaluated_properties_on_invalid_type(self):
         message = self.message_for(instance="foo", schema=schema)
         self.assertEqual(message, "'foo' is not of type 'object'")
 
+    def test_unevaluated_properties_on_invalid_inplace_applicators(self):
+        """Ensure that Draft 2020-12 11.3 is followed, per #1365."""
+        schema = {
+            "unevaluatedProperties": False,
+            "allOf": [
+                {"properties": {"foo": {"type": "string"}}},
+            ],
+        }
+        instance = {"foo": 1}
+
+        # cannot use `self.message_for`, which expects exactly one error
+        validators.Draft202012Validator.check_schema(schema)
+        validator = validators.Draft202012Validator(schema)
+        errors = list(validator.iter_errors(instance))
+        self.assertTrue(errors, msg=f"No errors were raised for {instance!r}")
+        self.assertEqual(
+            len(errors),
+            2,
+            msg=f"Expected exactly two errors, found {errors!r}",
+        )
+
+        messages = [error.message for error in errors]
+        expected = [
+            "1 is not of type 'string'",
+            "Unevaluated properties are not allowed ('foo' was unexpected)",
+        ]
+        self.assertEqual(set(messages), set(expected), "Unexpected messages")
+        self.assertEqual(messages, expected, "Keywords not evaluated in order")
+
     def test_single_item(self):
         schema = {"prefixItems": [{}], "items": False}
         message = self.message_for(
diff --git a/jsonschema/validators.py b/jsonschema/validators.py
index b8ca3bd45..d58740816 100644
--- a/jsonschema/validators.py
+++ b/jsonschema/validators.py
@@ -379,20 +379,31 @@ def iter_errors(self, instance, _schema=None):
                 )
                 return
 
-            for validator, k, v in validators:
-                errors = validator(self, v, instance, _schema) or ()
-                for error in errors:
-                    # set details if not already set by the called fn
-                    error._set(
-                        validator=k,
-                        validator_value=v,
-                        instance=instance,
-                        schema=_schema,
-                        type_checker=self.TYPE_CHECKER,
-                    )
-                    if k not in {"if", "$ref"}:
-                        error.schema_path.appendleft(k)
-                    yield error
+            todo = {k for _, k, _ in validators}
+            while todo:
+                dependent = []
+                for validator, k, v in validators:
+                    if isinstance(validator, _keywords.Keyword) \
+                            and todo.intersection(validator.needs):
+                        dependent.append([validator, k, v])
+                        continue
+                    errors = validator(self, v, instance, _schema) or ()
+                    for error in errors:
+                        # set details if not already set by the called fn
+                        error._set(
+                            validator=k,
+                            validator_value=v,
+                            instance=instance,
+                            schema=_schema,
+                            type_checker=self.TYPE_CHECKER,
+                        )
+                        if k not in {"if", "$ref"}:
+                            error.schema_path.appendleft(k)
+                        yield error
+                    todo.discard(k)
+                if dependent == validators:
+                    raise ValueError("Circular dependency between keywords")
+                validators = dependent
 
         def descend(
             self,