Large language models can produce toxic or inappropriate text even for benign inputs, creating risks when deployed at scale. Detoxification is therefore important for safety and user trust, particularly when we want to reduce harmful content without sacrificing the model's generation quality. Many existing approaches rely on model retraining, gradients, or learned auxiliary components, which can be costly and may not transfer across model families or to truly black-box settings. We introduce a test-time procedure that approximates the gradient of completion toxicity with respect to the input embeddings and uses a small number of descent steps to steer generation toward less toxic continuations. This is achieved with zeroth-order optimization that requires only access to input embeddings, a toxicity scoring function, and forward evaluations of the model. Empirically, the approach delivers robust toxicity reductions across models and prompts and, in most settings, achieves the best overall toxicity-quality trade-off. More broadly, our work positions word embeddings as effective control variables and encourages wider use of black-box optimization to guide autoregressive language models toward scalable, safer text generation, without requiring any training or access to intermediate computations.