In the downlink of a wireless LAN, power-save mode is a typical method to reduce power consumption. However, it usually causes large delay. Recently, remote wake-up control via a low-power wake-up radio (WuR) has been introduced to activate a node to instantly receive packets from an access point (AP). But link quality is not taken into account and protocol overhead of wake-up per node is relatively large. To solve these problems, in this paper, a broadcast-based wake-up control framework is proposed, and a low-power WuR is used to receive traffic indication map from an AP, monitor link quality, and perform carrier sense. Among the nodes which have packets buffered at the AP, only those whose SNR is above a threshold will be activated, contending via a proper contention window to receive packets from the AP. Optimal SNR threshold, deduced by theoretical analysis, helps to reduce transmission collisions and false wake-ups (caused by wake-up latency) and improve transmission rate. Extensive simulations confirm that the proposed method (i) effectively reduces power consumption of nodes compared with other methods, (ii) has less delay than power-save mode in times of light traffic, and (iii) achieves higher throughput than other methods in the saturation state.