Emotions guide human decisions, but whether large language models (LLMs) use emotion similarly remains unknown. We tested this using altruistic third-party punishment, where an observer incurs a personal cost to enforce fairness, a hallmark of human morality and often driven by negative emotion. In a large-scale comparison of 4,068 LLM agents with 1,159 adults across 796,100 decisions, LLMs used emotion to guide punishment, sometimes even more strongly than humans did: Unfairness elicited stronger negative emotion that led to more punishment; punishing unfairness produced more positive emotion than accepting; and critically, prompting self-reports of emotion causally increased punishment. However, mechanisms diverged: LLMs prioritized emotion over cost, enforcing norms in an almost all-or-none manner with reduced cost sensitivity, whereas humans balanced fairness and cost. Notably, reasoning models (o3-mini, DeepSeek-R1) were more cost-sensitive and closer to human behavior than foundation models (GPT-3.5, DeepSeek-V3), yet remained heavily emotion-driven. These findings provide the first causal evidence of emotion-guided moral decisions in LLMs and reveal deficits in cost calibration and nuanced fairness judgements, reminiscent of early-stage human responses. We propose that LLMs progress along a trajectory paralleling human development; future models should integrate emotion with context-sensitive reasoning to achieve human-like emotional intelligence.