While multi-fingered dexterous robot hands have the potential to provide human-level dexterity, using them for functional manipulation remains difficult because task success depends on precise contact, coordinated arm-hand motion, and reactive recovery from execution errors. Precise contact depends on complex contact dynamics that are difficult to model accurately in simulation, motivating real-world learning. However, real-world demonstrations in the full arm-hand control space are costly and noisy because each trajectory must coordinate arm motion with high-DoF multi-finger contact. Small execution deviations can further cause slipped contact or premature force application, making recovery from off-nominal contact states important for robust execution. To deal with these challenges, we propose HiFun, a hierarchical real-world RL framework for functional dexterous manipulation tasks. Our key insight is to decouple the control complexity into a functional hand skill for precise contact execution and an arm-hand coordination policy for arm control and hand-skill activation. This design enables effective real-time human intervention for reactive recovery learning and efficient data collection with Dynamic Movement Primitive (DMP) augmentation. Across six real-world tasks on two dexterous hands, HiFun achieves 98.3% average success within one hour of online training and remains robust to dynamic disturbances. The project page is available at https://hly-123.github.io/HiFun/.

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