Large Language Models (LLMs) have been augmented with web search to overcome the limitations of the static knowledge boundary by accessing up-to-date information from the open Internet. While this integration enhances model capability, it also introduces a distinct safety threat surface: the retrieval and citation process has the potential risk of exposing users to harmful or low-credibility web content. Existing red-teaming methods are largely designed for standalone LLMs as they primarily focus on unsafe generation, ignoring risks emerging from the complex search workflow. To address this gap, we propose CREST-Search, a pioneering red-teaming framework for LLMs with web search. The cornerstone of CREST-Search is three novel attack strategies that generate seemingly benign search queries yet induce unsafe citations. It also employs an iterative in-context refinement mechanism to strengthen adversarial effectiveness under black-box constraints. In addition, we construct a search-specific harmful dataset, WebSearch-Harm, which enables fine-tuning a specialized red-teaming model to improve query quality. Our experiments demonstrate that CREST-Search can effectively bypass safety filters and systematically expose vulnerabilities in web search-based LLM systems, underscoring the necessity of the development of robust search models.