Vibration reduction in axial piston pumps remains challenging due to the difficulty in identifying dominant transfer paths without extensive experimental data. This study proposes a novel power-based transfer path contribution methodology to achieve significant vibration mitigation within the pump system. Firstly, an experimentally validated dynamic model with 4 lumped mass points and 19 degrees of freedom is developed to systematically investigate vibration transmission mechanisms. Based on this theoretical model, we introduce a power-based ranking algorithm to quantitatively evaluate the contributions of dynamic movements and transfer paths to the overall vibration response. Results reveal that the end-cover is the primary radiating component, with rotational motion around the X EC axis being the dominant contributor to total vibration power. Theoretical transfer path analyses further identify PEC1 (cylinder force) and PEC3 (housing force) as the dominant vibration power transmission paths to the end-cover, while PEC2 (shaft force) also contributes significantly at specific frequencies. Based on these insights, a transfer path analysis (TPA)-guided optimization strategy combined with the single-objective genetic algorithm (GA) is implemented to minimize total vibration power by tuning the structural configuration and stiffness parameters of key connection components. The proposed method achieves substantial vibration reduction in the end-cover across multiple frequency bands and yields notable system-level improvements, including reduced housing vibration around the X H axis. These findings validate the theoretical foundation and demonstrate the practical value of the proposed approach for vibration control in hydraulic pumps.