Heteroresistance - in which a clonal bacterial population contains a cell subpopulation with higher resistance to antibiotics than the main population - is a growing clinical problem that complicates susceptibility determination and threatens therapeutic success. Despite the high prevalence of heteroresistance in clinical settings, the underlying genetic mechanisms that stably maintain heterogeneous bacterial populations are poorly understood. Using fluorescence microscopy, single-cell microfluidics, and quantitative image analysis, we show that random replication and segregation of multicopy plasmids produce populations of bacterium Escherichia coli MG1655 in which cells with low- and high-plasmid copy numbers stably co-exist. By combining stochastic simulations of a computational model with high-throughput single-cell measurements of blaTEM-1 expression, we show that copy number variability confers the bacterial population with transient resistance to a lethal concentration of a beta-lactam antibiotic. Moreover, this surviving, high plasmid copy minority is capable of regenerating a heterogeneous bacterial population with low and high plasmid copy numbers through segregational instability, rapidly alleviating the fitness burden of carrying large numbers of plasmids. Our results provide further support for the tenet that plasmids are more than simple vehicles for horizontal transmission of genetic information between cells, as they can also drive bacterial adaptation in dynamic environments by providing a platform for rapid amplification and attenuation of gene copy number that can accelerate the rate of resistance adaptation and can lead to treatment failure.