Fluctuations in gene expression give cells access to a spectrum of phenotypes that can temporarily increase drug resistance and serve as a transient basis for natural selection. To take full advantage of this noise-induced drug resistance, cells may rely on mechanisms that (1) increase cell-to-cell variability in gene expression, and (2) enable inheritance of beneficial gene expression states from one generation to the next. The ATP-binding cassette (ABC) protein family is a large group of membrane transporters that are conserved from bacteria to humans, and facilitate drug resistance by driving the secretion of substances from the cell interior. In budding yeast, the expression of the ABC transporter Pdr5p, and of several other pleiotropic drug response (PDR) pumps, is controlled by a coherent feedforward loop involving the partially redundant transcriptional regulators Pdr1p and Pdr3p. Here, we demonstrate that transcriptional regulation by coherent feedforward loops can enhance drug resistance by increasing cell-to-cell variability in gene expression, and by enabling prolonged activation of gene expression in response to transient signals. Our results highlight how mechanisms enabling transient, non-genetic inheritance may play important roles in defining the effectiveness of drug treatment.