We describe a novel technique for stabilizing frequency shifts in laser-interrogated vapor-cell atomic clocks. The method suppresses frequency shifts due to changes in the laser frequency, intensity, and modulation index as well as atomic vapor density. The clock operating parameters are monitored by using the atoms themselves, rather than by using conventional schemes for laser frequency and cell temperature control. The experiment is realized using a chip-scale atomic clock. The novel atomic-based stabilization approach results in a simpler setup and improved long-term performance.