We present a simple method for diode laser frequency stabilization that makes use of a Doppler-broadened vapor cell absorption signals of two frequency-shifted laser beams. Using second-order-diffracted, double-passed beams from an acousto-optic modulator, we achieve a frequency separation roughly equal to the Doppler half width. The differential transmission signals of the two beams provide an error signal with a very large linear feature, allowing frequency stabilization over a range of greater than 1 GHz by means of standard proportional-integral-derivative servo feedback to the piezoelectric control of the grating in our external cavity diode laser. We have applied this technique to two different diode laser systems, one used to lock to the 410 nm E1 transition in indium and another for locking to the M1/E2 transition in thallium at 1283 nm. In both cases the technique reduces frequency fluctuation to roughly 1 MHz over time scales from 10(-3) to 10(2) s.