The widespread adoption of Large Language Models (LLMs) has enabled diverse applications with very different latency requirements. Existing LLM serving frameworks rely on siloed infrastructure with coarse-grained workload segregation -- interactive and batch -- leading to inefficient resource utilization and limited support for fine-grained Quality-of-Service (QoS) differentiation. This results in operational inefficiencies, over-provisioning and poor load management during traffic surges. We present Niyama, a novel QoS-driven inference serving system that enables efficient co-scheduling of diverse workloads on shared infrastructure. Niyama introduces fine-grained QoS classification allowing applications to specify precise latency requirements, and dynamically adapts scheduling decisions based on real-time system state. Leveraging the predictable execution characteristics of LLM inference, Niyama implements a dynamic chunking mechanism to improve overall throughput while maintaining strict QoS guarantees. Additionally, Niyama employs a hybrid prioritization policy that balances fairness and efficiency, and employs selective request relegation that enables graceful service degradation during overload conditions. Our evaluation demonstrates that Niyama increases serving capacity by 32% compared to current siloed deployments, while maintaining QoS guarantees. Notably, under extreme load, our system reduces SLO violations by an order of magnitude compared to current strategies.