This paper presents a novel dual-microphone speech enhancement algorithm to improve noise robustness of hotword (wake-word) detection as a special application of keyword spotting. It exploits two unique properties of hotwords: they are leading phrases of valid voice queries that we intend to respond and have short durations. Consequently an STFT-based adaptive noise cancellation method modified to use deferred filter coefficients is proposed to extract hotwords out from stereo noisy microphone signals. The new algorithm is tested with two considerably different neural hotword detectors. Both systems have significantly reduced the false-reject rate when background has strong TV noise.