A major challenge in biology is that genetically identical cells in the same environment can display gene expression stochasticity (noise), which contributes to bet-hedging, drug tolerance, and cell-fate switching. The magnitude and timescales of stochastic fluctuations can depend on the gene regulatory network. Currently, it is unclear how gene expression noise of specific networks impacts the evolution of drug resistance in mammalian cells. Answering this question requires adjusting network noise independently from mean expression. Here, we develop positive and negative feedback-based synthetic gene circuits to decouple noise from the mean for Puromycin resistance gene expression in Chinese Hamster Ovary cells. In low Puromycin concentrations, the high-noise, positive-feedback network delays long-term adaptation, whereas it facilitates adaptation under high Puromycin concentration. Accordingly, the low-noise, negative-feedback circuit can maintain resistance by acquiring mutations while the positive-feedback circuit remains mutation-free and regains drug sensitivity. These findings may have profound implications for chemotherapeutic inefficiency and cancer relapse.