Robust 3D point-cloud recognition is critical for robotics, mapping, and urban sensing, yet point-cloud classifiers often suffer performance drops under domain shifts caused by sensor changes, environmental variation, and acquisition artifacts. Many existing adaptation methods are difficult to deploy in practice because they require access to source data or the internal parameters of the source model, which may be restricted by privacy, licensing, or security constraints. We present 3D-BBDA, a backpropagation-free black-box domain adaptation framework that adapts a source-trained predictor to unlabeled target data using only black-box outputs. Our method performs pseudo-label guided prototype-based alignment and employs a weighted prediction module to fuse source logits with alignment logits, reducing sensitivity to noisy pseudo-labels. To stabilize prototype memory when pseudo-label coverage is incomplete, we construct a Gaussian-perturbed prototype prior from unlabeled target predictions and use it as a fallback for missing or unreliable class prototypes during alignment. Experiments on four corrupted 3D benchmarks demonstrate consistent improvements over strong baselines. On ModelNet-40C, 3D-BBDA achieves mean errors of 32.08% (PointNet) and 29.62% (GDANet), outperforming Source-only (35.88% / 34.03%) and BFTT3D (33.78% / 32.36%). 3D-BBDA requires only a single forward pass with no gradient updates making it suitable for real-time, privacy-preserving deployment in transferable 3D recognition pipelines. Project page is available at https://visdomlab.github.io/3D_BBDA

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