Efficient power management of the radio is a critical requirement for the battery-operated portable electronic devices incorporating wireless transceivers to have a longer runtime. The power management function of IEEE 802.11 wireless local area networks (WLANs) allows stations (STAs) to operate in the doze mode to save energy significantly. In this paper, the enhanced timer-based power management (E-TPM) scheme, which supports the applications with delay-intolerant uplink traffic (DIUT), is presented for infrastructure IEEE 802.11 WLANs. With E-TPM, the radio transceiver of the dozing STA is woken up right away when an outgoing frame is generated by the STA so that DIUT is transmitted in a timely manner. In addition, a novel model for stochastic analysis of the E-TPM is developed. Based on this model, the probabilities that an STA is active, idle, or dozing are derived, and the power consumption of the STA, the number of frames buffered at the access point (AP) for the STA operating in doze mode, and the average delay per frame are obtained. These results enable an efficient power management algorithm that optimizes the idle timer and doze duration at the STA so that the doze mode does not result in extra delay in DIUT, and the delay of downlink traffic is controlled within a given bound. Numerical results show that the proposed E-TPM is able to considerably reduce delay with limited available memory space at the AP.