Large Language Models (LLMs) play a critical role in emerging agentic applications, where the timely completion of each entire inference is critical. Meanwhile, agentic LLM inferences are increasingly served on heterogeneous GPUs in operator's resource pools. Therefore, it is crucial to route incoming inference requests to appropriate GPUs so that their end-to-end latency requirements are satisfied whenever possible, thereby achieving high goodput. In this paper, we propose GoodServe, a goodput-optimized serving system for agentic inferences over heterogeneous resources. GoodServe performs inference routing in a predict-and-rectify manner. It estimates the request output lengths as well as the GPU serving status in an accurate and also practical manner. Based on information from both the demand and resource sides, it then makes high-quality routing decisions using a just-enough instance selection heuristic. It also periodically monitors SLO-violation risks of active requests and triggers runtime request migrations to address unexpected dynamics. Our evaluations show that GoodServe improves goodput by up to 27.4% over existing routing methods.