Large language models (LLMs) often produce content that contradicts or overlooks information provided in the input context, a phenomenon known as faithfulness hallucination. In this paper, we propose Context-Fidelity Boosting (CFB), a lightweight and general decoding-time framework that effectively reduces such hallucinations by boosting the generation probability of context-relevant tokens. Motivated by logit-shaping principles in watermarking techniques, CFB leverages token-level logit adjustments based on their presence or salience in the input context. Specifically, we develop three boosting strategies, static, context-aware, and token-aware that progressively incorporate distributional divergence, attention scores, and semantic similarity. Notably, CFB requires no retraining or architectural changes, making it compatible with a wide range of LLMs. Experiments on summarization and question answering tasks across multiple open-source LLMs show that CFB consistently improves faithfulness metrics, with minimal generation overhead. Our implementation is fully open-sourced.