Modern servers employ multiple resource management algorithms, including fast core schedulers and overload controllers to balance application performance and resource utilization. Individual algorithms and their amalgamation are required to meet these tight performance requirements. In this paper, we demonstrate that state-of-the-art core schedulers and overload controllers produce poor performance when deployed simultaneously. Fundamentally, the design assumptions of each controller are violated by the other controller. An overload controller assumes that all resources are dedicated to an application, while a core scheduler assumes that all incoming load will be admitted. To overcome this fundamental limitation, we present CoreSync, a server-driven credit-based protocol for joint core scheduling and overload control. CoreSync relies on the basic idea that the admitted load should be proportional to the allocated resources. However, strict proportionality can lead to low utilization when admitted load does not materialize at the server (e.g., when demand drops). Thus, CoreSync uses partial proportionality to balance latency, throughput, and utilization. Our evaluation across synthetic and real-world workloads shows that CoreSync outperforms state-of-the-art schedulers and overload controllers. In particular, in overload scenarios, CoreSync improves throughput by up to 6%. At low loads, CoreSync reduces the 99th percentile latency by up to 1.7× and improves CPU utilization by up to 1.4×.