Large Language Models (LLMs) frequently exhibit performance degradation in specialized domains due to distribution shifts. While unsupervised Test-Time Adaptation (TTA) offers a lightweight solution, existing methods suffer from critical flaws: input-centric adaptation lacks reasoning constraints, while output-centric optimization falls into a "Confidence Trap" of reinforced hallucinations. We instead study Few-Shot Anchored TTA, where a small labeled support set is available, and propose Anchor-Tethered Test-Time Adaptation (AT-TTA), a framework that synergizes linguistic alignment with reliable reasoning. AT-TTA employs Dual-View Uncertainty Calibration, minimizing input perplexity for domain alignment and sequence-level output energy for generation consistency. Furthermore, to mitigate catastrophic drift, we construct a "Semantic Anchor" by fine-tuning on the labeled support set and its filtered augmentations, which serves as a stable domain prior and constrains the adaptation trajectory via an Energy-Guided Adaptive Replay strategy. Extensive experiments on the AdaptEval benchmark demonstrate strong performance across diverse domains, effectively preventing model collapse while maintaining high inference efficiency.