Radio duty cycling is a commonly employed mechanism to support long-term sustainable operations of WSNs. Combined with the effect of unreliable wireless links, many challenges arise for ensuring delay bounded data delivery with reliability constraint. However, research on energy-efficient data forwarding with statistical delay bound in duty-cycled WSNs still remains unaddressed. This paper proposes EDGE, a novel opportunistic forwarding technique tailored for duty-cycled WSNs with unreliable wireless links. The key idea is to exploit the available path diversity to minimize the transmission cost while providing statistical delay guarantees. Delay quantiles are derived at each node in a distributed manner and are used as the guidelines in forwarding decision making, so that an early arriving packet will be opportunistically switched to the energy-optimal path for communication cost minimization. Comprehensive evaluation results show that EDGE effectively reduces the transmission cost with statistical delay guarantees under various network settings.