The keyhole phenomenon, i.e., uncorrelated but rank-deficient fading, can lead to significant performance degradations in multiple-input multiple-output (MIMO) systems and has to be carefully taken into account for system design. In this paper, considering the practically important case of two transmit and an arbitrary number of receive antennas, we provide a simple closed-form expression for the asymptotic pairwise error probability (PEP) of space-time codes (STCs) in generalized keyhole fading channels including Rayleigh, Ricean, Nakagami-q, Nakagami-m, and Weibull fading. We show how the number of transmit and receive antennas as well as the fading parameters affect the diversity gain. The presented analysis provides new insights into STC design and can be used to obtain tight asymptotic upper bounds for the bit, symbol, and frame error probabilities of arbitrary STCs in keyhole fading.