The spread of antibiotic resistance is an emerging health crisis. Here, we demonstrate that phage predation can increase the transfer and proliferation of plasmid-encoded antibiotic resistance during surface-associated growth by reshaping microbial spatial organization. Using two strains of the bacterium Escherichia coli where one is a plasmid donor and the other a potential recipient, we demonstrate that phage predation slows the spatial demixing of the strains. This increases the number of cell-cell contacts and the extent of plasmid transfer between them. The underlying mechanism is that phage predation shifts the region of maximal cell growth from the biomass periphery to the interior where cell movement is highly constrained. This creates straighter interfaces between the strains that are less likely to coalesce with neighboring interfaces, thus slowing spatial demixing and enhancing plasmid transfer. Our results demonstrate that phage predation can promote the spread of antibiotic resistance with implications for phage therapy.