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We investigate optimal resource allocation and power management in virtualized data centers with time-varying workloads and heterogeneous applications. Prior work in this area uses prediction based approaches for resource provisioning. In this work, we take an alternate approach that makes use of the queueing information available in the system to make online control decisions. Specifically, we use the recently developed technique of Lyapunov Optimization to design an online admission control, routing, and resource allocation algorithm for a virtualized data center. This algorithm maximizes a joint utility of the average application throughput and energy costs of the data center. Our approach is adaptive to unpredictable changes in the workload and does not require estimation and prediction of its statistics.