Document understanding aims to perform question answering and information extraction over document images, where the visual content is highly information-dense and most queries rely on only a few relevant layout regions. However, existing methods either adopt a one-pass strategy that implicitly assumes all layouts are equally important, or focus excessively on small regions at the cost of losing critical layout information. To address these limitations, we introduce Doc-CoB (Chain-of-Boxes), a simple-yet-effective framework that integrates coarse-to-fine layout-aware visual reasoning into multimodal large language models. Instead of directly zooming into small regions, Doc-CoB progressively focuses on query-relevant layouts while preserving global document information. Specifically, it first selects key layout boxes and then focuses on them for further understanding with visual prompting. To support this paradigm, we introduce two reasoning tasks for box recognition and box reasoning, with an automatic pipeline that constructs 249k training samples with intermediate visual supervision. Extensive experiments on seven benchmarks with four popular models show that Doc-CoB significantly improves performance, demonstrating its effectiveness and wide applicability.