Retrieval-Augmented Generation (RAG) effectively improves the accuracy of Large Language Models (LLMs). However, retrieval noises significantly undermine the quality of LLMs' generation, necessitating the development of denoising mechanisms. Previous works extract evidence straightforwardly without deep thinking, which may risk filtering out key clues and struggle with generalization. To this end, we propose EviOmni, which learns to extract rational evidence via reasoning first and then extracting. Specifically, EviOmni integrates evidence reasoning and evidence extraction into one unified trajectory, followed by knowledge token masking to avoid information leakage, optimized via on-policy reinforcement learning with verifiable rewards in terms of answer, length, and format. Extensive experiments on five benchmark datasets show the superiority of EviOmni, which provides compact and high-quality evidence, enhances the accuracy of downstream tasks, and supports both traditional and agentic RAG systems.