In wireless sensor networks for monitoring and control applications, a sink node needs to disseminate messages to all nodes to acquire monitoring data or to control the operation of sensor nodes. The basic flooding protocol suffers from low transmission reliability in broadcasting messages due to the hidden terminal problem. Besides, it can cause the broadcast storm problem by having many nodes rebroadcast the received message simultaneously. In order to resolve these problems while minimizing energy consumption in delivery of broadcast messages, we propose a reliable slotted broadcast protocol (RSBP) that allocates broadcast time slots to nodes based on their slot demands and then allows every node to transmit its broadcast message within the allocated slots. Then, every node can broadcast messages safely in a contention-free manner. Moreover, RSBP can be deployed easily since it does not have any specific requirements such as GPS, multi-channels and directional antennas that may not be always available in real scenarios. We show by experimental study that RSBP significantly outperforms other broadcast protocols in terms of safety-critical packet delivery and energy consumption.