Object Goal Navigation (ObjectNav) in unknown environments presents significant challenges, particularly in Open-Vocabulary Mobile Manipulation (OVMM), where robots must efficiently explore large spaces, locate small objects, and accurately position themselves for subsequent manipulation. Existing approaches struggle to meet these demands: rule-based methods offer structured exploration but lack adaptability, while reinforcement learning (RL)-based methods enhance adaptability but fail to ensure effective long-term navigation. Moreover, both approaches often overlook precise stopping positions, which are critical for successful manipulation.To address these challenges, we propose APRR (Active Perception Meets Rule-Guided RL), a two-phase framework that designs a new rule-guided RL policy for the exploration phase and a novel active target perception policy for the last-mile navigation phase. Inspired by human search behavior, our rule-guided RL policy enables efficient and adaptive exploration by combining structured heuristics with learning-based decision-making. In the last-mile navigation phase, we introduce an RL-based policy enhanced with active target perception, allowing the robot to refine its position dynamically based on real-time detection feedback. Experimental results demonstrate that APRR improves the success rate by 13\%, significantly outperforming existing methods. Furthermore, real-world experiments validate the practicality and effectiveness of APRR in real-world mobile manipulation scenarios, offering a robust and adaptable solution for precise object navigation. The code is available at https://anonymous.4open.science/r/APRR-B582.