Autonomous browsing agents powered by large language models (LLMs) are increasingly used to automate web-based tasks. However, their reliance on dynamic content, tool execution, and user-provided data exposes them to a broad attack surface. This paper presents a comprehensive security evaluation of such agents, focusing on systemic vulnerabilities across multiple architectural layers. Our work outlines the first end-to-end threat model for browsing agents and provides actionable guidance for securing their deployment in real-world environments. To address discovered threats, we propose a defense in depth strategy incorporating input sanitization, planner executor isolation, formal analyzers, and session safeguards. These measures protect against both initial access and post exploitation attack vectors. Through a white box analysis of a popular open source project, Browser Use, we demonstrate how untrusted web content can hijack agent behavior and lead to critical security breaches. Our findings include prompt injection, domain validation bypass, and credential exfiltration, evidenced by a disclosed CVE and a working proof of concept exploit.