LiDAR-based 3D object detection has seen impressive advances in recent times. However, deploying trained 3D detectors in the real world often yields unsatisfactory performance when the distribution of the test data significantly deviates from the training data due to different weather conditions, object sizes, \textit{etc}. A key factor in this performance degradation is the diminished generalizability of pre-trained models, which creates a sharp loss landscape during training. Such sharpness, when encountered during testing, can precipitate significant performance declines, even with minor data variations. To address the aforementioned challenges, we propose \textbf{dual-perturbation optimization (DPO)} for \textbf{\underline{T}est-\underline{t}ime \underline{A}daptation in \underline{3}D \underline{O}bject \underline{D}etection (TTA-3OD)}. We minimize the sharpness to cultivate a flat loss landscape to ensure model resiliency to minor data variations, thereby enhancing the generalization of the adaptation process. To fully capture the inherent variability of the test point clouds, we further introduce adversarial perturbation to the input BEV features to better simulate the noisy test environment. As the dual perturbation strategy relies on trustworthy supervision signals, we utilize a reliable Hungarian matcher to filter out pseudo-labels sensitive to perturbations. Additionally, we introduce early Hungarian cutoff to avoid error accumulation from incorrect pseudo-labels by halting the adaptation process. Extensive experiments across three types of transfer tasks demonstrate that the proposed DPO significantly surpasses previous state-of-the-art approaches, specifically on Waymo $\rightarrow$ KITTI, outperforming the most competitive baseline by 57.72\% in $\text{AP}_\text{3D}$ and reaching 91\% of the fully supervised upper bound.