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Generative Adversarial Networks (GANs) with style-based generators (e.g. StyleGAN) successfully enable semantic control over image synthesis, and recent studies have also revealed that interpretable image translations could be obtained by modifying the latent code. However, in terms of the low-level image content, traveling in the latent space would lead to `spatially entangled changes' in corresponding images, which is undesirable in many real-world applications where local editing is required. To solve this problem, we analyze properties of the 'style space' and explore the possibility of controlling the local translation with pre-trained style-based generators. Concretely, we propose 'Style Intervention', a lightweight optimization-based algorithm which could adapt to arbitrary input images and render natural translation effects under flexible objectives. We verify the performance of the proposed framework in facial attribute editing on high-resolution images, where both photo-realism and consistency are required. Extensive qualitative results demonstrate the effectiveness of our method, and quantitative measurements also show that the proposed algorithm outperforms state-of-the-art benchmarks in various aspects.