CSMA is the de facto standard in wireless LANs (WLANs), where one transceiver is used for both the control and data planes. When many nodes contend to access a same channel, the WLAN transceiver performs carrier sense during most time, which wastes much energy. Dynamic adjustment of parameters (contention window) is suggested in previous works for improving network throughput, but this is also realized at the cost of continuously monitoring the channel with large power consumption. To solve these problems, in this paper, we suggest tightly integrating a lower power wake-up radio (WuR) with the power-hungry WLAN module. Specifically, (i) The WuR is used to monitor the channel and conduct carrier sense. It activates the WLAN module for actual transmissions when the channel gets ready. (ii) The WuR is used to measure the inter-frame space, based on which contention window is adjusted accordingly. Extensive simulation evaluations confirm that the proposed scheme (WuR-CSMA) effectively reduces the duty ratio of WLAN modules and improves system throughput, achieving both energy and spectral efficiency compared with the conventional schemes.