diff --git a/litellm/cost_calculator.py b/litellm/cost_calculator.py
index e358636c105..88aacdd30a6 100644
--- a/litellm/cost_calculator.py
+++ b/litellm/cost_calculator.py
@@ -812,6 +812,33 @@ def _cost_map_entry_prices_anything(entry: Mapping[str, object]) -> bool:
     )
 
 
+def _has_rate(model: str, custom_llm_provider: str | None) -> bool:
+    # A registered entry is a real answer even when it prices at zero; an unregistered
+    # model is not, because `get_model_info` invents zero rates for it rather than
+    # raising. Hence truthiness here, not `is not None`.
+    if model in litellm.model_cost:
+        return True
+    try:
+        info: Final = litellm.get_model_info(model=model, custom_llm_provider=custom_llm_provider)
+    except Exception:  # noqa: BLE001  # get_model_info raises bare Exception for some unmapped models
+        return False
+    return any(info.get(key) for key in ("input_cost_per_token", "output_cost_per_token", "input_cost_per_second"))
+
+
+def _priced_provider_response_model(
+    provider_response_model: str | None,
+    completion_response_model: str | None,
+    custom_llm_provider: str | None,
+) -> str | None:
+    if provider_response_model is None:
+        return None
+    if _has_rate(provider_response_model, custom_llm_provider):
+        return provider_response_model
+    if completion_response_model is not None and _has_rate(completion_response_model, custom_llm_provider):
+        return completion_response_model
+    return provider_response_model
+
+
 def _select_model_name_for_cost_calc(
     model: str | None,
     completion_response: object | None,
@@ -858,7 +885,15 @@ def _select_model_name_for_cost_calc(
             return_model = model
 
     elif base_model is not None or provider_response_model is not None:
-        return_model = base_model if base_model is not None else provider_response_model
+        return_model = (
+            base_model
+            if base_model is not None
+            else _priced_provider_response_model(
+                provider_response_model,
+                completion_response_model if isinstance(completion_response_model, str) else None,
+                custom_llm_provider,
+            )
+        )
 
     elif completion_response_model is None and hidden_params is not None:
         if hidden_params.get("model", None) is not None and len(hidden_params["model"]) > 0:
diff --git a/tests/unit/test_cost_calculator.py b/tests/unit/test_cost_calculator.py
index 36e188e82d6..51527851104 100644
--- a/tests/unit/test_cost_calculator.py
+++ b/tests/unit/test_cost_calculator.py
@@ -5639,3 +5639,72 @@ def test_completion_cost_bills_base_when_gemini_serves_on_demand(
     )
 
     assert cost == pytest.approx(100 * 0.001 + 50 * 0.002)
+
+
+def test_an_unpriced_provider_slug_does_not_bill_the_turn_at_zero():
+    """Regression test for #42161.
+
+    `_select_model_name_for_cost_calc` prefers `provider_response_model` over
+    `response.model`, and `get_model_info` answers a model it has never heard of with
+    zero rates instead of raising, so a turn reporting an unregistered slug was billed
+    0.0 with nothing in the logs to explain it. Anthropic hits this by naming the dated
+    build in `message_start` while the map carries the family.
+
+    The invariant: what the provider reports must not change the price of a turn the
+    price map cannot quote it by.
+    """
+    from litellm.cost_calculator import completion_cost
+    from litellm.types.utils import Choices, Message, ModelResponse, Usage
+
+    unpriced = "claude-test-42161"
+    assert unpriced not in litellm.model_cost
+
+    def _response(reported: str | None) -> ModelResponse:
+        response = ModelResponse(
+            model="anthropic/claude-opus-5",
+            choices=[Choices(message=Message(content="x"))],
+        )
+        response.usage = Usage(prompt_tokens=38, completion_tokens=24, total_tokens=62)
+        response._hidden_params = {} if reported is None else {"provider_response_model": reported}
+        return response
+
+    baseline = completion_cost(completion_response=_response(None), custom_llm_provider="anthropic")
+    assert baseline > 0
+
+    reported_unpriced = completion_cost(completion_response=_response(unpriced), custom_llm_provider="anthropic")
+    assert reported_unpriced == baseline
+
+
+def test_a_priced_provider_slug_still_decides_the_rate():
+    """The fallback must not cost the reported name its precedence.
+
+    When the provider names something the map does price, that is the most specific
+    truth about what served the turn and it still decides the rate.
+    """
+    from litellm.cost_calculator import completion_cost
+    from litellm.types.utils import Choices, Message, ModelResponse, Usage
+
+    priced = "test-model-priced-42161"
+    litellm.register_model(
+        model_cost={
+            priced: {
+                "input_cost_per_token": 1e-05,
+                "output_cost_per_token": 2e-05,
+                "litellm_provider": "anthropic",
+                "mode": "chat",
+            }
+        }
+    )
+
+    def _response(reported: str | None, model: str) -> ModelResponse:
+        response = ModelResponse(model=model, choices=[Choices(message=Message(content="x"))])
+        response.usage = Usage(prompt_tokens=38, completion_tokens=24, total_tokens=62)
+        response._hidden_params = {} if reported is None else {"provider_response_model": reported}
+        return response
+
+    reported = completion_cost(
+        completion_response=_response(priced, "anthropic/claude-opus-5"),
+        custom_llm_provider="anthropic",
+    )
+    expected = 38 * 1e-05 + 24 * 2e-05
+    assert reported == pytest.approx(expected)