Offline reinforcement learning (RL) is vulnerable to real-world data corruption, with even robust algorithms failing under challenging observation and mixture corruptions. We posit this failure stems from data corruption creating sharp minima in the loss landscape, leading to poor generalization. To address this, we are the first to apply Sharpness-Aware Minimization (SAM) as a general-purpose, plug-and-play optimizer for offline RL. SAM seeks flatter minima, guiding models to more robust parameter regions. We integrate SAM into strong baselines for data corruption: IQL, a top-performing offline RL algorithm in this setting, and RIQL, an algorithm designed specifically for data-corruption robustness. We evaluate them on D4RL benchmarks with both random and adversarial corruption. Our SAM-enhanced methods consistently and significantly outperform the original baselines. Visualizations of the reward surface confirm that SAM finds smoother solutions, providing strong evidence for its effectiveness in improving the robustness of offline RL agents.