This paper investigated the exponential synchronization (ES) problem of reaction-diffusion neural networks over directed networks under an asynchronous sampled-data event-triggered intermittent control scheme. By integrating event-triggered communication and intermittent control mechanisms, hybrid control framework was developed to reduce communication transmissions and control activation time. A Lyapunov–Krasovskii functional (LKF) involving historical-state integral terms was constructed, and sufficient synchronization conditions were derived using graph-theoretic techniques and inequality methods. The proposed criterion guaranteed exponential convergence of synchronization errors and avoided Zeno behavior. Numerical simulations demonstrated that the proposed strategy achieved satisfactory synchronization performance with reduced communication requirements.