Video relighting with background replacement is a challenging task critical for applications in film production and creative media. Existing methods struggle to balance temporal consistency, spatial fidelity, and illumination naturalness. To address these issues, we introduce FlowPortal, a novel training-free flow-based video relighting framework. Our core innovation is a Residual-Corrected Flow mechanism that transforms a standard flow-based model into an editing model, guaranteeing perfect reconstruction when input conditions are identical and enabling faithful relighting when they differ, resulting in high structural consistency. This is further enhanced by a Decoupled Condition Design for precise lighting control and a High-Frequency Transfer mechanism for detail preservation. Additionally, a masking strategy isolates foreground relighting from background pure generation process. Experiments demonstrate that FlowPortal achieves superior performance in temporal coherence, structural preservation, and lighting realism, while maintaining high efficiency. Project Page: https://gaowenshuo.github.io/FlowPortalProject/.