The search for suitable datasets is the critical "first step" in data-driven research, but it remains a great challenge. Researchers often need to search for datasets based on high-level task descriptions. However, existing search systems struggle with this task due to ambiguous user intent, task-to-dataset mapping and benchmark gaps, and entity ambiguity. To address these challenges, we introduce KATS, a novel end-to-end system for task-oriented dataset search from unstructured scientific literature. KATS consists of two key components, i.e., offline knowledge base construction and online query processing. The sophisticated offline pipeline automatically constructs a high-quality, dynamically updatable task-dataset knowledge graph by employing a collaborative multi-agent framework for information extraction, thereby filling the task-to-dataset mapping gap. To further address the challenge of entity ambiguity, a unique semantic-based mechanism is used for task entity linking and dataset entity resolution. For online retrieval, KATS utilizes a specialized hybrid query engine that combines vector search with graph-based ranking to generate highly relevant results. Additionally, we introduce CS-TDS, a tailored benchmark suite for evaluating task-oriented dataset search systems, addressing the critical gap in standardized evaluation. Experiments on our benchmark suite show that KATS significantly outperforms state-of-the-art retrieval-augmented generation frameworks in both effectiveness and efficiency, providing a robust blueprint for the next generation of dataset discovery systems.