The growing deployment of large language model (LLM) based agents that interact with external environments has created new attack surfaces for adversarial manipulation. One major threat is indirect prompt injection, where attackers embed malicious instructions in external environment output, causing agents to interpret and execute them as if they were legitimate prompts. While previous research has focused primarily on plain-text injection attacks, we find a significant yet underexplored vulnerability: LLMs' dependence on structured chat templates and their susceptibility to contextual manipulation through persuasive multi-turn dialogues. To this end, we introduce ChatInject, an attack that formats malicious payloads to mimic native chat templates, thereby exploiting the model's inherent instruction-following tendencies. Building on this foundation, we develop a persuasion-driven Multi-turn variant that primes the agent across conversational turns to accept and execute otherwise suspicious actions. Through comprehensive experiments across frontier LLMs, we demonstrate three critical findings: (1) ChatInject achieves significantly higher average attack success rates than traditional prompt injection methods, improving from 5.18% to 32.05% on AgentDojo and from 15.13% to 45.90% on InjecAgent, with multi-turn dialogues showing particularly strong performance at average 52.33% success rate on InjecAgent, (2) chat-template-based payloads demonstrate strong transferability across models and remain effective even against closed-source LLMs, despite their unknown template structures, and (3) existing prompt-based defenses are largely ineffective against this attack approach, especially against Multi-turn variants. These findings highlight vulnerabilities in current agent systems.