Model inversion attacks (MIAs) aim to reconstruct the private training data by accessing a public model, raising concerns about privacy leakage. Black-box MIAs, where attackers can only query the model and obtain outputs, are closer to real-world scenarios. The latest black-box attacks have outperformed the state-of-the-art white-box attacks, and existing defenses cannot resist them effectively. To fill this gap, we propose Stealthy Shield Defense (SSD), a post-processing algorithm against black-box MIAs. Our idea is to modify the model's outputs to minimize the conditional mutual information (CMI). We mathematically prove that CMI is a special case of information bottlenecks (IB), and thus inherits the advantages of IB---making predictions less dependent on inputs and more dependent on ground truths. This theoretically guarantees our effectiveness, both in resisting MIAs and preserving utility. For minimizing CMI, we formulate a convex optimization problem and solve it via the water-filling method. Adaptive rate-distortion is introduced to reduce the modification to the outputs, and the water-filling is implemented on GPUs to address computational cost. Without the need to retrain the model, our algorithm is plug-and-play and easy to deploy. Experimental results indicate that SSD outperforms existing defenses, in terms of MIA resistance and model's utility, across various attack algorithms, training datasets, and model architectures. Our code is available at https://github.com/ZhuangQu/Stealthy-Shield-Defense.