diff --git a/airflow/api_connexion/exceptions.py b/airflow/api_connexion/exceptions.py
index 0360ec2b67dbb..7f3623a656ef2 100644
--- a/airflow/api_connexion/exceptions.py
+++ b/airflow/api_connexion/exceptions.py
@@ -29,6 +29,7 @@
 EXCEPTIONS_LINK_MAP = {
     400: f"{doc_link}#section/Errors/BadRequest",
     404: f"{doc_link}#section/Errors/NotFound",
+    405: f"{doc_link}#section/Errors/MethodNotAllowed",
     401: f"{doc_link}#section/Errors/Unauthenticated",
     409: f"{doc_link}#section/Errors/AlreadyExists",
     403: f"{doc_link}#section/Errors/PermissionDenied",
diff --git a/airflow/api_connexion/openapi/v1.yaml b/airflow/api_connexion/openapi/v1.yaml
index cf84e6e2e3630..5b5a717f1f0ce 100644
--- a/airflow/api_connexion/openapi/v1.yaml
+++ b/airflow/api_connexion/openapi/v1.yaml
@@ -192,6 +192,8 @@ info:
     framing, or deceptive request routing). To resolve this, please ensure that your syntax is correct.
     ## NotFound
     This client error response indicates that the server cannot find the requested resource.
+    ## MethodNotAllowed
+    Indicates that the request method is known by the server but is not supported by the target resource.
     ## NotAcceptable
     The target resource does not have a current representation that would be acceptable to the user
     agent, according to the proactive negotiation header fields received in the request, and the
@@ -2796,6 +2798,13 @@ components:
         application/json:
           schema:
             $ref: '#/components/schemas/Error'
+    # 405
+    'MethodNotAllowed':
+      description: Request method is known by the server but is not supported by the target resource.
+      content:
+        application/json:
+          schema:
+            $ref: '#/components/schemas/Error'
     # 406
     'NotAcceptable':
       description: A specified Accept header is not allowed.
diff --git a/airflow/www/extensions/init_views.py b/airflow/www/extensions/init_views.py
index 56753cc369bcc..11a0d083ee644 100644
--- a/airflow/www/extensions/init_views.py
+++ b/airflow/www/extensions/init_views.py
@@ -20,7 +20,7 @@
 
 import connexion
 from connexion import ProblemException
-from flask import Flask
+from flask import Flask, request
 
 from airflow.api_connexion.exceptions import common_error_handler
 from airflow.security import permissions
@@ -135,11 +135,27 @@ def init_error_handlers(app: Flask):
 
 def init_api_connexion(app: Flask) -> None:
     """Initialize Stable API"""
+    base_path = '/api/v1'
+
+    from airflow.www import views
+
+    @app.errorhandler(404)
+    @app.errorhandler(405)
+    def _handle_api_error(ex):
+        if request.path.startswith(base_path):
+            # 404 errors are never handled on the blueprint level
+            # unless raised from a view func so actual 404 errors,
+            # i.e. "no route for it" defined, need to be handled
+            # here on the application level
+            return common_error_handler(ex)
+        else:
+            return views.circles(ex)
+
     spec_dir = path.join(ROOT_APP_DIR, 'api_connexion', 'openapi')
     connexion_app = connexion.App(__name__, specification_dir=spec_dir, skip_error_handlers=True)
     connexion_app.app = app
     api_bp = connexion_app.add_api(
-        specification='v1.yaml', base_path='/api/v1', validate_responses=True, strict_validation=True
+        specification='v1.yaml', base_path=base_path, validate_responses=True, strict_validation=True
     ).blueprint
     app.register_error_handler(ProblemException, common_error_handler)
     app.extensions['csrf'].exempt(api_bp)
diff --git a/tests/api_connexion/test_error_handling.py b/tests/api_connexion/test_error_handling.py
new file mode 100644
index 0000000000000..e921aea88f41d
--- /dev/null
+++ b/tests/api_connexion/test_error_handling.py
@@ -0,0 +1,52 @@
+# Licensed to the Apache Software Foundation (ASF) under one
+# or more contributor license agreements.  See the NOTICE file
+# distributed with this work for additional information
+# regarding copyright ownership.  The ASF licenses this file
+# to you under the Apache License, Version 2.0 (the
+# "License"); you may not use this file except in compliance
+# with the License.  You may obtain a copy of the License at
+#
+#   http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing,
+# software distributed under the License is distributed on an
+# "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+# KIND, either express or implied.  See the License for the
+# specific language governing permissions and limitations
+# under the License.
+import unittest
+
+from airflow.www import app
+
+
+class TestErrorHandling(unittest.TestCase):
+    @classmethod
+    def setUpClass(cls) -> None:
+        super().setUpClass()
+        cls.app = app.create_app(testing=True)  # type:ignore
+
+    def setUp(self) -> None:
+        self.client = self.app.test_client()  # type:ignore
+
+    def test_incorrect_endpoint_should_return_json(self):
+
+        # Given we have application with Connexion added
+        # When we hitting incorrect endpoint in API path
+
+        resp_json = self.client.get("/api/v1/incorrect_endpoint").json
+
+        # Then we have parsable JSON as output
+
+        self.assertEqual(404, resp_json["status"])
+
+        # When we are hitting non-api incorrect enpoint
+
+        resp_json = self.client.get("/incorrect_endpoint").json
+
+        # Then we do not have JSON as response, rather standard HTML
+
+        self.assertIsNone(resp_json)
+
+        resp_json = self.client.put("/api/v1/variables").json
+
+        self.assertEqual('Method Not Allowed', resp_json["title"])