Knowledge graphs (KGs) are the cornerstone of the semantic web, offering up-to-date representations of real-world entities and relations. Yet large language models (LLMs) remain largely static after pre-training, causing their internal knowledge to become outdated and limiting their utility in time-sensitive web applications. To bridge this gap between dynamic knowledge and static models, a prevalent approach is to enhance LLMs with KGs. However, prevailing methods typically rely on parameter-invasive fine-tuning, which risks catastrophic forgetting and often degrades LLMs' general capabilities. Moreover, their static integration frameworks cannot keep pace with the continuous evolution of real-world KGs, hindering their deployment in dynamic web environments. To bridge this gap, we introduce KGA (\textit{\underline{K}nowledge \underline{G}raph-guided \underline{A}ttention}), a novel framework that dynamically integrates external KGs into LLMs exclusively at inference-time without any parameter modification. Inspired by research on neuroscience, we rewire the self-attention module by innovatively introducing two synergistic pathways: a \textit{bottom-up knowledge fusion} pathway and a \textit{top-down attention guidance} pathway. The \textit{bottom-up pathway} dynamically integrates external knowledge into input representations via input-driven KG fusion, which is akin to the \textit{stimulus-driven attention process} in the human brain. Complementarily, the \textit{top-down pathway} aims to assess the contextual relevance of each triple through a \textit{goal-directed verification process}, thereby suppressing task-irrelevant signals and amplifying knowledge-relevant patterns. By synergistically combining these two pathways, our method supports real-time knowledge fusion. Extensive experiments on four benchmarks verify KGA's strong fusion performance and efficiency.