Treatment strategies for infectious disease often aim to rapidly clear the pathogen population in hopes of minimizing the potential for antibiotic resistance. However, a number of recent studies highlight the potential of alternative strategies that attempt to inhibit the growth of resistant pathogens by maintaining a competing population of drug-sensitive cells. Unfortunately, to date there is little direct experimental evidence that drug sensitive cells can be leveraged to enhance antibiotic containment strategies. In this work, we combine in vitro experiments in computer-controlled bioreactors with simple mathematical models to show that drug-sensitive cells can enhance our ability to control bacterial populations with antibiotics. To do so, we measured the "escape time" required for drug-resistant E. coli populations to eclipse a threshold density maintained by adaptive antibiotic dosing. While populations containing only resistant cells rapidly escape containment, we found that matched populations with sensitive cells added could be contained for significantly longer. The increase in escape time occurs only when the threshold density-the acceptable bacterial burden-is sufficiently high, an effect that mathematical models attribute to increased competition. The results provide direct experimental evidence linking the presence of sensitive cells to improved control of microbial populations.