diff --git a/fastapi/openapi/utils.py b/fastapi/openapi/utils.py
index 8f1852b0cc..f7238bac89 100644
--- a/fastapi/openapi/utils.py
+++ b/fastapi/openapi/utils.py
@@ -242,7 +242,14 @@ def get_openapi_operation_metadata(
     operation["summary"] = generate_operation_summary(route=route, method=method)
     if route.description:
         operation["description"] = route.description
-    operation_id = route.operation_id or route.unique_id
+    if route.operation_id:
+        operation_id = route.operation_id
+    elif route.methods and len(route.methods) > 1:
+        # Multi-method routes: unique_id uses first method only; use method-specific id
+        base = route.unique_id.rsplit("_", 1)[0]
+        operation_id = f"{base}_{method.lower()}"
+    else:
+        operation_id = route.unique_id
     if operation_id in operation_ids:
         endpoint_name = getattr(route.endpoint, "__name__", "<unnamed_endpoint>")
         message = f"Duplicate Operation ID {operation_id} for function {endpoint_name}"
diff --git a/tests/test_generate_unique_id_function.py b/tests/test_generate_unique_id_function.py
index c56e6d5794..2a4038b00f 100644
--- a/tests/test_generate_unique_id_function.py
+++ b/tests/test_generate_unique_id_function.py
@@ -1697,3 +1697,24 @@ def test_warn_duplicate_operation_id():
         ]
         assert len(duplicate_warnings) > 0
         assert "Duplicate Operation ID" in str(duplicate_warnings[0].message)
+
+
+def test_multiple_methods_unique_operation_id():
+    """Regression test for #13175: routes with multiple methods get unique operation IDs."""
+    app = FastAPI()
+
+    def clear():
+        return {"ok": True}
+
+    app.add_api_route("/clear", clear, methods=["POST", "DELETE"])
+    client = TestClient(app)
+    with warnings.catch_warnings(record=True) as w:
+        warnings.simplefilter("always")
+        response = client.get("/openapi.json")
+        assert len([x for x in w if "Duplicate Operation ID" in str(getattr(x, "message", ""))]) == 0
+    paths = response.json()["paths"]["/clear"]
+    post_id = paths["post"]["operationId"]
+    delete_id = paths["delete"]["operationId"]
+    assert post_id != delete_id
+    assert post_id.endswith("_post")
+    assert delete_id.endswith("_delete")