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With the tremendous growth of cloud computing and Internet-scale online services, massive geographically distributed infrastructures have been deployed to meet the increasing demand, resulting in significant monetary expenditure and environmental pollution caused by energy consumption. In this paper, we investigate how to minimize the long-term energy cost of dynamic Internet-scale systems by fully exploiting the energy efficiency in geographic diversity and variation over time. To this end, we formulate a stochastic optimization problem by considering the fundamental uncertainties of Internet-scale systems, such as the dynamic data. We develop a dynamic request mapping algorithm to solve the formulated problem, which balances the tradeoff between energy cost and delay performance. Our designed algorithm makes real-time decisions based on current queue backlogs and system states, and does not require any knowledge of stochastic job arrivals and service rates caused by dynamic data queries. We formally prove the optimality of our approach. Extensive trace-driven simulations verify our theoretical analysis and demonstrate that our algorithm outperforms the baseline strategies with respect to system cost, queue backlogs, and delay.