diff --git a/sentry_sdk/integrations/falcon.py b/sentry_sdk/integrations/falcon.py
index 9b3cc40cd6..3fab11cfeb 100644
--- a/sentry_sdk/integrations/falcon.py
+++ b/sentry_sdk/integrations/falcon.py
@@ -175,17 +175,25 @@ def sentry_patched_handle_exception(self, *args):
         # NOTE(jmagnusson): falcon 2.0 changed falcon.API._handle_exception
         # method signature from `(ex, req, resp, params)` to
         # `(req, resp, ex, params)`
-        if isinstance(args[0], Exception):
-            ex = args[0]
-        else:
-            ex = args[2]
+        ex = response = None
+        with capture_internal_exceptions():
+            ex = next(argument for argument in args if isinstance(argument, Exception))
+            response = next(
+                argument for argument in args if isinstance(argument, falcon.Response)
+            )
 
         was_handled = original_handle_exception(self, *args)
 
+        if ex is None or response is None:
+            # Both ex and response should have a non-None value at this point; otherwise,
+            # there is an error with the SDK that will have been captured in the
+            # capture_internal_exceptions block above.
+            return was_handled
+
         hub = Hub.current
         integration = hub.get_integration(FalconIntegration)
 
-        if integration is not None and _exception_leads_to_http_5xx(ex):
+        if integration is not None and _exception_leads_to_http_5xx(ex, response):
             # If an integration is there, a client has to be there.
             client = hub.client  # type: Any
 
@@ -225,15 +233,28 @@ def sentry_patched_prepare_middleware(
     falcon_helpers.prepare_middleware = sentry_patched_prepare_middleware
 
 
-def _exception_leads_to_http_5xx(ex):
-    # type: (Exception) -> bool
+def _exception_leads_to_http_5xx(ex, response):
+    # type: (Exception, falcon.Response) -> bool
     is_server_error = isinstance(ex, falcon.HTTPError) and (ex.status or "").startswith(
         "5"
     )
     is_unhandled_error = not isinstance(
         ex, (falcon.HTTPError, falcon.http_status.HTTPStatus)
     )
-    return is_server_error or is_unhandled_error
+
+    # We only check the HTTP status on Falcon 3 because in Falcon 2, the status on the response
+    # at the stage where we capture it is listed as 200, even though we would expect to see a 500
+    # status. Since at the time of this change, Falcon 2 is ca. 4 years old, we have decided to
+    # only perform this check on Falcon 3+, despite the risk that some handled errors might be
+    # reported to Sentry as unhandled on Falcon 2.
+    return (is_server_error or is_unhandled_error) and (
+        not FALCON3 or _has_http_5xx_status(response)
+    )
+
+
+def _has_http_5xx_status(response):
+    # type: (falcon.Response) -> bool
+    return response.status.startswith("5")
 
 
 def _set_transaction_name_and_source(event, transaction_style, request):
diff --git a/tests/integrations/falcon/test_falcon.py b/tests/integrations/falcon/test_falcon.py
index 19b56c749a..65140a9fd7 100644
--- a/tests/integrations/falcon/test_falcon.py
+++ b/tests/integrations/falcon/test_falcon.py
@@ -9,6 +9,7 @@
 import sentry_sdk
 from sentry_sdk.integrations.falcon import FalconIntegration
 from sentry_sdk.integrations.logging import LoggingIntegration
+from sentry_sdk.utils import parse_version
 
 
 try:
@@ -19,6 +20,9 @@
     import falcon.inspect  # We only need this module for the ASGI test
 
 
+FALCON_VERSION = parse_version(falcon.__version__)
+
+
 @pytest.fixture
 def make_app(sentry_init):
     def inner():
@@ -32,9 +36,22 @@ def on_get(self, req, resp, message_id):
                 sentry_sdk.capture_message("hi")
                 resp.media = "hi"
 
+        class CustomError(Exception):
+            pass
+
+        class CustomErrorResource:
+            def on_get(self, req, resp):
+                raise CustomError()
+
+        def custom_error_handler(*args, **kwargs):
+            raise falcon.HTTPError(status=falcon.HTTP_400)
+
         app = falcon.API()
         app.add_route("/message", MessageResource())
         app.add_route("/message/{message_id:int}", MessageByIdResource())
+        app.add_route("/custom-error", CustomErrorResource())
+
+        app.add_error_handler(CustomError, custom_error_handler)
 
         return app
 
@@ -418,3 +435,23 @@ def test_falcon_not_breaking_asgi(sentry_init):
         falcon.inspect.inspect_app(asgi_app)
     except TypeError:
         pytest.fail("Falcon integration causing errors in ASGI apps.")
+
+
+@pytest.mark.skipif(
+    (FALCON_VERSION or ()) < (3,),
+    reason="The Sentry Falcon integration only supports custom error handlers on Falcon 3+",
+)
+def test_falcon_custom_error_handler(sentry_init, make_app, capture_events):
+    """
+    When a custom error handler handles what otherwise would have resulted in a 5xx error,
+    changing the HTTP status to a non-5xx status, no error event should be sent to Sentry.
+    """
+    sentry_init(integrations=[FalconIntegration()])
+    events = capture_events()
+
+    app = make_app()
+    client = falcon.testing.TestClient(app)
+
+    client.simulate_get("/custom-error")
+
+    assert len(events) == 0
diff --git a/tox.ini b/tox.ini
index 7a212561b9..d2741320c3 100644
--- a/tox.ini
+++ b/tox.ini
@@ -81,6 +81,7 @@ envlist =
     {py2.7,py3.5,py3.6,py3.7}-falcon-v{1.4}
     {py2.7,py3.5,py3.6,py3.7}-falcon-v{2.0}
     {py3.5,py3.6,py3.7,py3.8,py3.9,py3.10,py3.11}-falcon-v{3.0}
+    {py3.7,py3.8,py3.9,py3.10,py3.11}-falcon-v{3.1}
 
     # FastAPI
     {py3.7,py3.8,py3.9,py3.10,py3.11}-fastapi
@@ -312,6 +313,7 @@ deps =
     falcon-v1.4: falcon>=1.4,<1.5
     falcon-v2.0: falcon>=2.0.0rc3,<3.0
     falcon-v3.0: falcon>=3.0.0,<3.1.0
+    falcon-v3.1: falcon>=3.1.0,<3.2
 
     # FastAPI
     fastapi: fastapi