With the fast expansion of the Internet of Things (IoT), a vast number of IoT gateways are being deployed and continuously disseminating data to proximate devices. As one of the most prevalent wireless technologies in our daily work and life, WiFi has been extensively used for data dissemination because of the widespread availability of WiFi infrastructures. However, data transmission over high-power WiFi can quickly deplete the batteries of IoT devices. Despite the introduction of numerous power saving protocols in WiFi-based IoT computer network systems, achieving both high energy efficiency and low delay remains a challenge due to the unpredictability of data traffic. To address this, we propose a dual-radio Dual-constraint Node Activation (DNA) scheduling scheme, which leverages an auxiliary low-power ZigBee radio to reactively activate the high-power WiFi radio for energy-efficient data dissemination. Besides the delay constraint required by WiFi upper-layer applications, the dual-radio energy optimization problem studied in this work is also limited by the constrained ZigBee bandwidth for performing radio activation. By jointly scheduling dual-radio duty cycles, DNA dynamically allocates ZigBee bandwidth to balance energy and delay for optimized system performance. Extensive real-world testing was conducted on a prototype dual-radio system equipped with off-the-shelf ZigBee and WiFi radios. Under medium bandwidth and delay constraints, DNA achieves an energy consumption of 7.95 mJ per data packet, which is 95.4% and 36.2% lower than the WiFi’s standard power saving protocol and a contemporary dual-radio scheduling scheme, respectively. Additionally, DNA has demonstrated superior reliability and adaptability in various scenarios.