Video Anomaly Detection~(VAD) focuses on identifying anomalies within videos. Supervised methods require an amount of in-domain training data and often struggle to generalize to unseen anomalies. In contrast, training-free methods leverage the intrinsic world knowledge of large language models (LLMs) to detect anomalies but face challenges in localizing fine-grained visual transitions and diverse events. Therefore, we propose EventVAD, an event-aware video anomaly detection framework that combines tailored dynamic graph architectures and multimodal LLMs through temporal-event reasoning. Specifically, EventVAD first employs dynamic spatiotemporal graph modeling with time-decay constraints to capture event-aware video features. Then, it performs adaptive noise filtering and uses signal ratio thresholding to detect event boundaries via unsupervised statistical features. The statistical boundary detection module reduces the complexity of processing long videos for MLLMs and improves their temporal reasoning through event consistency. Finally, it utilizes a hierarchical prompting strategy to guide MLLMs in performing reasoning before determining final decisions. We conducted extensive experiments on the UCF-Crime and XD-Violence datasets. The results demonstrate that EventVAD with a 7B MLLM achieves state-of-the-art (SOTA) in training-free settings, outperforming strong baselines that use 7B or larger MLLMs.