Key Information Extraction (KIE) from visually-rich documents (VrDs) is a critical task, for which recent Large Language Models (LLMs) and Multi-Modal Large Language Models (MLLMs) have demonstrated strong potential. However, their reliance on autoregressive inference, which generates outputs sequentially, creates a significant efficiency bottleneck, especially as KIE tasks often involve extracting multiple, semantically independent fields. To overcome this limitation, we introduce PIP: a Parallel Inference Paradigm for KIE. Our approach reformulates the problem by using "[mask]" tokens as placeholders for all target values, enabling their simultaneous generation in a single forward pass. To facilitate this paradigm, we develop a tailored mask pre-training strategy and construct large-scale supervised datasets. Experimental results show that our PIP-models achieve a 5-36x inference speedup with negligible performance degradation compared to traditional autoregressive base models. By substantially improving efficiency while maintaining high accuracy, PIP paves the way for scalable and practical real-world KIE solutions.