Existing large language models (LLMs) have shown remarkable progress in dialogue systems. However, many approaches still overlook the fundamental role of events throughout multi-turn interactions, leading to \textbf{incomplete context tracking}. Without tracking these events, dialogue systems often lose coherence and miss subtle shifts in user intent, causing disjointed responses. To bridge this gap, we present \textbf{EventWeave}, an event-centric framework that identifies and updates both core and supporting events as the conversation unfolds. Specifically, we organize these events into a dynamic event graph, which represents the interplay between \textbf{core events} that shape the primary idea and \textbf{supporting events} that provide critical context during the whole dialogue. By leveraging this dynamic graph, EventWeave helps models focus on the most relevant events when generating responses, thus avoiding repeated visits of the entire dialogue history. Experimental results on two benchmark datasets show that EventWeave improves response quality and event relevance without fine-tuning.