Decisions on how to best optimize energy systems operations are becoming ever so complex and conflicting, that model-based predictive control (MPC) algorithms must play an important role. However, a key factor prohibiting the widespread adoption of MPC in buildings, is the cost, time, and effort associated with learning first-principles based dynamical models of the underlying physical system. This paper introduces an alternative approach for implementing finite-time receding horizon control using control-oriented data-driven models. We call this approach Data Predictive Control (DPC). Specifically, by utilizing separation of variables, two novel algorithms for implementing DPC using a single regression tree and with regression trees ensembles (random forest) are presented. The data predictive controller enables the building operator to trade off energy consumption against thermal comfort without having to learn white/grey box models of the systems dynamics. We present a comprehensive numerical study which compares the performance of DPC with an MPC based energy management strategy, using a single zone building model. Our results demonstrate that performance of DPC is comparable to an MPC controller, with only 3.8% additional cost in terms of optimal objective function and within 95% in terms of R2 score, thereby making it an alluring alternative to MPC, whenever the associated cost of learning the model is high.