Understanding whether large language models (LLMs) and the human brain converge on similar computational principles remains a fundamental and important question in cognitive neuroscience and AI. Do the brain-like patterns observed in LLMs emerge simply from scaling, or do they reflect deeper alignment with the architecture of human language processing? This study focuses on the sentence-level neural mechanisms of language models, systematically investigating how layer-wise representations in LLMs align with the dynamic neural responses during human sentence comprehension. By comparing hierarchical embeddings from 14 publicly available LLMs with fMRI data collected from participants, who were exposed to a naturalistic narrative story, we constructed sentence-level neural prediction models to identify the model layers most significantly correlated with brain region activations. Results show that improvements in model performance drive the evolution of representational architectures toward brain-like hierarchies, particularly achieving stronger functional and anatomical correspondence at higher semantic abstraction levels. These findings advance our understanding of the computational parallels between LLMs and the human brain, highlighting the potential of LLMs as models for human language processing.