Bacteriophage (phage) are both predators and evolutionary drivers for bacteria, notably contributing to the spread of antimicrobial resistance (AMR) genes by generalized transduction. Our current understanding of this complex relationship is limited. We used an interdisciplinary approach to quantify how these interacting dynamics can lead to the evolution of multidrug-resistant bacteria. We cocultured two strains of methicillin-resistant Staphylococcus aureus, each harboring a different antibiotic resistance gene, with generalized transducing phage. After a growth phase of 8 h, bacteria and phage surprisingly coexisted at a stable equilibrium in our culture, the level of which was dependent on the starting concentration of phage. We detected double-resistant bacteria as early as 7 h, indicating that transduction of AMR genes had occurred. We developed multiple mathematical models of the bacteria and phage relationship and found that phage-bacteria dynamics were best captured by a model in which phage burst size decreases as the bacteria population reaches stationary phase and where phage predation is frequency-dependent. We estimated that one in every 108 new phage generated was a transducing phage carrying an AMR gene and that double-resistant bacteria were always predominantly generated by transduction rather than by growth. Our results suggest a shift in how we understand and model phage-bacteria dynamics. Although rates of generalized transduction could be interpreted as too rare to be significant, they are sufficient in our system to consistently lead to the evolution of multidrug-resistant bacteria. Currently, the potential of phage to contribute to the growing burden of AMR is likely underestimated. IMPORTANCE Bacteriophage (phage), viruses that can infect and kill bacteria, are being investigated through phage therapy as a potential solution to the threat of antimicrobial resistance (AMR). In reality, however, phage are also natural drivers of bacterial evolution by transduction when they accidentally carry nonphage DNA between bacteria. Using laboratory work and mathematical models, we show that transduction leads to evolution of multidrug-resistant bacteria in less than 8 h and that phage production decreases when bacterial growth decreases, allowing bacteria and phage to coexist at stable equilibria. The joint dynamics of phage predation and transduction lead to complex interactions with bacteria, which must be clarified to prevent phage from contributing to the spread of AMR.