Broadcasting delay-sensitive information over a duty-cycled wireless sensor network is considered, and a cluster-based protocol is proposed. The proposed protocol, namely Broadcast over Duty-Cycle and LEACH (BOD-LEACH), takes advantage of the LEACH’s energy-efficient clustering. This approach shifts the total burden of energy consumption of a single cluster head by rotating the cluster-head role among all nodes in the network. It also permits the ordinary (member) nodes in a cluster to turn off their radios whenever they enter inactive TDMA slots. However, LEACH does not consider broadcast messages, and the member nodes scheduling is established as a sequence of Time Division Multiple Access (TDMA) without any common active period. A broadcast message should then be postponed to the next TDMA schedule and transmitted in a sequence of unicast messages, which is inefficient in terms of latency, bandwidth occupation, and power consumption. The proposed protocol adds new common static and dynamic broadcast periods to support and accelerate broadcasting. The dynamic periods are scheduled following the past arrivals of messages and using a Markov chain model. To our knowledge, this work is the first that proposes the use of clustering to perform simultaneous local broadcasts at several clusters. This reduces broadcast latency and ensures scalability. The protocol has been simulated, numerically analyzed, and compared with LEACH. The results show clear improvement over LEACH with regard to broadcast latency, at a low energy cost.