We demonstrate a variation of pump-probe spectroscopy that is particularly useful for laser frequency stabilization. The polarization-enhanced absorption spectroscopy (POLEAS) signal provides a significant improvement in signal-to-noise ratio over saturated absorption spectroscopy (SAS) for the important and commonly used atomic cycling transitions. The improvements can directly increase the short-term stability of a laser frequency lock, given sufficient servo loop bandwidth. The long-term stability of the POLEAS method, which is limited by environmental sensitivities, is comparable to that of SAS. The POLEAS signal is automatically Doppler-free, without requiring a separate Doppler subtraction beam, and lends itself to straightforward compact packaging. Finally, by increasing the amplitude of the desired (cycling) peak, while reducing the amplitude of all other peaks in the manifold, the POLEAS method eases the implementation of laser auto-locking schemes.