This paper proposes a super-twisting sliding-mode control (STSMC) strategy to enhance the efficiency and stability of a heaving point absorber wave energy converter (PAWEC) system equipped with a permanent magnet synchronous generator (PMSG). In particular, the STSMC is designed to address both generator-side and grid-side control challenges by ensuring precise regulation under varying wave conditions. A dynamical model of the PAWEC is developed to describe system responses, while the power take-off (PTO) mechanism is tailored to maintain consistent generator speed and efficient energy conversion. Lyapunov stability theory is employed to verify the stability of the proposed controller. Simulation studies and tests on a small-scale experimental setup with a 500 W PAWEC model under regular and irregular waves demonstrate that STSMC improves generator speed regulation and power output by more than 30% compared to field-oriented control (FOC), nonlinear adaptive backstepping (NAB), and first-order sliding-mode control (FOSMC). The proposed approach also manages grid-side total harmonic distortion (THD) effectively, keeping it below 5%. These results indicate that STSMC can substantially improve the dynamic performance and energy efficiency of wave energy systems.