In VR interactions with embodied conversational agents, users' emotional intent is often conveyed more by how something is said than by what is said. However, most VR agent pipelines rely on speech-to-text processing, discarding prosodic cues and often producing emotionally incongruent responses despite correct semantics. We propose an emotion-context-aware VR interaction pipeline that treats vocal emotion as explicit dialogue context in an LLM-based conversational agent. A real-time speech emotion recognition model infers users' emotional states from prosody, and the resulting emotion labels are injected into the agent's dialogue context to shape response tone and style. Results from a within-subjects VR study (N=30) show significant improvements in dialogue quality, naturalness, engagement, rapport, and human-likeness, with 93.3% of participants preferring the emotion-aware agent.