Microprocessors may need to keep most of their cores off in the era of dark silicon due to thermal constraints. Recent studies have proposed Computational Sprinting, which allows a chip to temporarily exceed its power and thermal limits by turning on all its cores for a short time period, such that its computing performance is boosted for bursty computation demands. However, conducting sprinting in a data center faces new challenges due to power and thermal constraints at the data center level, which are exacerbated by recently proposed power infrastructure under-provisioning and reliance on renewable energy, as well as the increasing server density. In this paper, we propose Data Center Sprinting, a methodology that enables a data center to temporarily boost its computing performance by turning on more cores in the era of dark silicon, in order to handle occasional workload bursts. We demonstrate the feasibility of this approach by analyzing the tripping characteristics of data center circuit breakers and the discharging characteristics of energy storage devices, in order to realize safe sprinting without causing undesired server overheating or shutdown. We evaluate a prototype of Data Center Sprinting on a hardware testbed and in data enter-level simulations. The experimental results show that our solution can improve the average computing performance of a data center by a factor of 1.62 to 2.45 for 5 to 30 minutes.