Zero-shot object navigation (ZSON) in unseen environments remains a challenging problem for household robots, requiring strong perceptual understanding and decision-making capabilities. While recent methods leverage metric maps and Large Language Models (LLMs), they often depend on depth sensors or prebuilt maps, limiting the spatial reasoning ability of Multimodal Large Language Models (MLLMs). Mapless ZSON approaches have emerged to address this, but they typically make short-sighted decisions, leading to local deadlocks due to a lack of historical context. We propose PanoNav, a fully RGB-only, mapless ZSON framework that integrates a Panoramic Scene Parsing module to unlock the spatial parsing potential of MLLMs from panoramic RGB inputs, and a Memory-guided Decision-Making mechanism enhanced by a Dynamic Bounded Memory Queue to incorporate exploration history and avoid local deadlocks. Experiments on the public navigation benchmark show that PanoNav significantly outperforms representative baselines in both SR and SPL metrics.