Sleep staging is essential for diagnosing sleep disorders and assessing neurological health. Existing automatic methods typically extract features from complex polysomnography (PSG) signals and train domain-specific models, which often lack intuitiveness and require large, specialized datasets. To overcome these limitations, we introduce a new paradigm for sleep staging that leverages large multimodal general-purpose models to emulate clinical diagnostic practices. Specifically, we convert raw one-dimensional PSG time-series into intuitive two-dimensional waveform images and then fine-tune a multimodal large model to learn from these representations. Experiments on three public datasets (ISRUC, MASS, SHHS) demonstrate that our approach enables general-purpose models, without prior exposure to sleep data, to acquire robust staging capabilities. Moreover, explanation analysis reveals our model learned to mimic the visual diagnostic workflow of human experts for sleep staging by PSG images. The proposed method consistently outperforms state-of-the-art baselines in accuracy and robustness, highlighting its efficiency and practical value for medical applications. The code for the signal-to-image pipeline and the PSG image dataset will be released.