diff --git a/fastapi/openapi/utils.py b/fastapi/openapi/utils.py
index 828442559b..de99aa90ac 100644
--- a/fastapi/openapi/utils.py
+++ b/fastapi/openapi/utils.py
@@ -243,7 +243,16 @@ 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
+    else:
+        # If the route has multiple methods, generate a unique operation_id
+        # using the current method to avoid duplicates
+        assert route.methods is not None
+        if len(route.methods) > 1:
+            operation_id = f"{route.unique_id}_{method.lower()}"
+        else:
+            operation_id = route.unique_id
     if operation_id in operation_ids:
         message = (
             f"Duplicate Operation ID {operation_id} for function "
diff --git a/tests/test_multiple_methods_unique_id.py b/tests/test_multiple_methods_unique_id.py
new file mode 100644
index 0000000000..11be625a78
--- /dev/null
+++ b/tests/test_multiple_methods_unique_id.py
@@ -0,0 +1,52 @@
+"""
+Test that routes with multiple methods get unique operation IDs.
+This is a regression test for issue #13175.
+"""
+import warnings
+
+from fastapi import FastAPI
+from fastapi.testclient import TestClient
+
+
+def test_multiple_methods_generate_unique_operation_ids():
+    """Test that add_api_route with multiple methods generates unique operation IDs."""
+    app = FastAPI()
+
+    def clear():
+        return {"cleared": True}
+
+    app.add_api_route("/clear", clear, methods=["POST", "DELETE"])
+
+    # Capture warnings to check for duplicate operation_id warnings
+    with warnings.catch_warnings(record=True) as w:
+        warnings.simplefilter("always")
+        client = TestClient(app)
+        response = client.get("/openapi.json")
+        
+        # There should be no duplicate operation_id warnings
+        dup_warnings = [
+            warning for warning in w 
+            if "Duplicate Operation ID" in str(warning.message)
+        ]
+        assert len(dup_warnings) == 0, f"Expected no duplicate warnings, got: {dup_warnings}"
+
+    openapi_schema = response.json()
+    
+    # Get the operation IDs for POST and DELETE
+    post_operation_id = openapi_schema["paths"]["/clear"]["post"]["operationId"]
+    delete_operation_id = openapi_schema["paths"]["/clear"]["delete"]["operationId"]
+    
+    # They should be different
+    assert post_operation_id != delete_operation_id, (
+        f"POST and DELETE should have different operation IDs. "
+        f"Got POST: {post_operation_id}, DELETE: {delete_operation_id}"
+    )
+    
+    # Verify the operation IDs contain the correct method suffix
+    assert post_operation_id.endswith("_post"), f"POST operation_id should end with '_post', got: {post_operation_id}"
+    assert delete_operation_id.endswith("_delete"), f"DELETE operation_id should end with '_delete', got: {delete_operation_id}"
+
+
+if __name__ == "__main__":
+    test_multiple_methods_generate_unique_operation_ids()
+    print("Test passed!")