Network virtualization, as a key driver for revenue enhancement, is under deep exploration by the communication society. Elastic optical network is a growing inter-data center communication solution whose flexible nature facilitates commercial implementation of virtualization concepts. Flexibility and virtuality are two main pillars of efficient networking which meet in a virtualized inter-data center elastic optical network and their interwoven management can significantly reduce the power consumption of data center networks, as a significant energy-consuming contributor. An efficient resource allocation is required to harvest the expected gain of a virtualized network. We propose a power-efficient joint dynamic resource allocation scheme, which optimally allocates computation and communication resources in an inter-data center elastic optical network. The scheme incorporates the benefits of conventional offline and online resource allocation schemes and reduces the power consumption by 19% compared to its traditional counterparts while keeping the delay and service outage below their desired thresholds. The proposed scheme not only supports traffic streams with distinguished service requirements but also exploits the involved service differentiation to further improve power efficiency. Strikingly, in a typical scenario where delaysensitive and delay-tolerant services co-exist, the reduction in power consumption can be enhanced up to 50%. The efficiency is further improved for a higher number of delay-tolerant services with more relaxed delay requirement. The proposed scheme provides an intelligent compromise between service outage and service requirements under tough networking conditions such that the service requirements of the delaysensitive services are maintained for the least number of dropped bits in the delay-tolerant services.