Recent advances in diffusion models enable high-quality video generation and editing, but precise relighting with consistent video contents, which is critical for shaping scene atmosphere and viewer attention, remains unexplored. Mainstream text-to-video (T2V) models lack fine-grained lighting control due to text's inherent limitation in describing lighting details and insufficient pre-training on lighting-related prompts. Additionally, constructing high-quality relighting training data is challenging, as real-world controllable lighting data is scarce. To address these issues, we propose RelightMaster, a novel framework for accurate and controllable video relighting. First, we build RelightVideo, the first dataset with identical dynamic content under varying precise lighting conditions based on the Unreal Engine. Then, we introduce Multi-plane Light Image (MPLI), a novel visual prompt inspired by Multi-Plane Image (MPI). MPLI models lighting via K depth-aligned planes, representing 3D light source positions, intensities, and colors while supporting multi-source scenarios and generalizing to unseen light setups. Third, we design a Light Image Adapter that seamlessly injects MPLI into pre-trained Video Diffusion Transformers (DiT): it compresses MPLI via a pre-trained Video VAE and injects latent light features into DiT blocks, leveraging the base model's generative prior without catastrophic forgetting. Experiments show that RelightMaster generates physically plausible lighting and shadows and preserves original scene content. Demos are available at https://wkbian.github.io/Projects/RelightMaster/.