Real-world systems often encounter new data over time, which leads to experiencing target domain shifts. Existing Test-Time Adaptation (TTA) methods tend to apply computationally heavy and memory-intensive backpropagation-based approaches to handle this. Here, we propose a novel method that uses a backpropagation-free approach for TTA for the specific case of 3D data. Our model uses a two-stream architecture to maintain knowledge about the source domain as well as complementary target-domain-specific information. The backpropagation-free property of our model helps address the well-known forgetting problem and mitigates the error accumulation issue. The proposed method also eliminates the need for the usually noisy process of pseudo-labeling and reliance on costly self-supervised training. Moreover, our method leverages subspace learning, effectively reducing the distribution variance between the two domains. Furthermore, the source-domain-specific and the target-domain-specific streams are aligned using a novel entropy-based adaptive fusion strategy. Extensive experiments on popular benchmarks demonstrate the effectiveness of our method. The code will be available at https://github.com/abie-e/BFTT3D.