We report a simple scheme for stabilizing and tuning the length of a conventional piezo-driven optical cavity against the resonant transmission of a master laser. In contrast with other schemes, we drive the piezo at its mechanical resonance of 5 kHz over an amplitude equivalent to one free spectral range and use a feedback circuit that incorporates phase-sensitive detection of the master-laser transmission. The bandwidth of our cavity-lock circuit is limited only by the resonance frequency of the cavity piezo and is 1.4 kHz. The stabilized mean cavity length reaches in 30 s a minimum Allan deviation of approximately 10 kHz (a length stability of 20 parts per trillion) equaling that of the polarization-stabilized He-Ne we use as our master laser. Here, we investigate the mechanical characteristics of the cavity, describe the lock circuit and its measured performance, and provide simple analytical relations between the phase-sensitive signal and cavity displacement. Our setup economizes the cost and amount of equipment necessary for stabilizing multiple continuous-wave lasers operating at different wavelengths.