Wireless sensor networks (WSN) are becoming a pervasive technology integrated in most of real-time monitoring infrastructures and industrial control applications. Timeliness accuracy, performance and energy efficiency are key metrics to consider when deploying such WSN systems. Timeliness accuracy amounts to time-stamp collected data at sensor level in order to calculate an integrated real-time state of the monitored environment. It is usually achieved on the expense of energy consumption of sensors. Namely, such metrics are conflicting in a way that improving one metric deteriorates the other metrics. This paper proposes an energy-efficient time synchronization protocol to enable a high accuracy calibration for time stamping sensors data. The rational behind the protocol is to ensure that data is correctly time-stamped and timerelevant in order to operate the control loop managing the energy of the smart building. Our experimental results on an actual case study show that our protocol outperforms the state of the art protocols in terms of both time accuracy and energy efficiency.