LLM inference latency critically determines user experience and operational costs, directly impacting throughput under SLO constraints. Even brief latency spikes degrade service quality despite acceptable average performance. However, distributed inference environments featuring diverse software frameworks and XPU architectures combined with dynamic workloads make latency analysis challenging. Constrained by intrusive designs that necessitate service restarts or even suspension, and by hardware-bound implementations that fail to adapt to heterogeneous inference environments, existing AI profiling methods are often inadequate for real-time production analysis. We present LatencyPrism, the first zero-intrusion multi-platform latency sculpting system. It aims to break down the inference latency across pipeline, proactively alert on inference latency anomalies, and guarantee adherence to SLOs, all without requiring code modifications or service restarts. LatencyPrism has been deployed across thousands of XPUs for over six months. It enables low-overhead real-time monitoring at batch level with alerts triggered in milliseconds. This approach distinguishes between workload-driven latency variations and anomalies indicating underlying issues with an F1-score of 0.98. We also conduct extensive experiments and investigations into root cause analysis to demonstrate LatencyPrism's capability. Furthermore, we introduce the first LLM anomaly simulation toolkit to facilitate future research in robust and predictable inference systems.